Attachment 'quickref-linalg-tr.tex'
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l.48 \begin{document}
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l.49 \begin{multicols*}
{3}
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<recently read> \url
l.56 \url
{http://wiki.sagemath.org/quickref}\\
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l.68 {\warn
Uyarı}: Bir vektörün ilk indisi $0$'dır.\\
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l.70 {\ex
\verb!u = vector(QQ, [1, 3/2, -1])!} $= (1,\frac{3}{2},-1) \in \mat...
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l.70 ..., -1])!} $= (1,\frac{3}{2},-1) \in \mathbb
{Q}^3$ \\
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l.71 {\ex
\verb!v = vector(QQ, {2:4, 95:4, 210:0})!}\\
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l.78 {\ex
\verb!u = vector(QQ, [1, 3/2, -1])!}\\
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l.79 {\ex
\verb!v = vector(ZZ, [1, 8, -2])!}\\
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l.81 {\ex
\verb!2*u - 3*v!} doÄŸrusal bileÅŸim\\
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l.82 {\ex
\verb!u.dot_product(v)!} \\
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l.83 {\ex
\verb!u.dot_product(v)!} iç çarpım\\
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l.85 {\ex
\verb!u.cross_product(v)!} sıralama: \verb!u!$\times$\verb!v!\\
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l.87 {\ex
\verb!u.inner_product(v)!} u'nun anasından gelen iç çarpım\\
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l.89 {\ex
\verb!u.pairwise_product(v)!} $=(u_0v_0, u_1v_1, u_2v_2, \ldots)$ \\
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l.91 {\ex
\verb!u.norm() == u.norm(2)!} Öklid normu\\
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l.93 {\ex
\verb!u.norm(1)!} kutu içeriklerinin toplamı\\
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l.95 {\ex
\verb!u.norm(Infinity)!} en büyük kutu içeriği\\
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l.97 {\ex
\verb!A.gram_schmidt()!} \verb!A! matrisinin satırlarını dönüÅ...
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l.103 {\warn
Uyarı}: Satır ve sütunların isimlendirilmesi 0'dan başlar\\
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l.104 {\ex
\verb!A = matrix(ZZ, [[1,2],[3,4],[5,6]])!}\\
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l.107 {\ex
\verb!B = matrix(QQ, 2, [1,2,3,4,5,6])!}\\
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l.110 {\ex
\verb!C = matrix(CDF, 2, 2, [[5*I, 4*I], [I, 6]])!}\\
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l.114 {\ex
\verb!Z = matrix(QQ, 2, 2, 0)!} sıfır matris\\
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\verb!D = matrix(QQ, 2, 2, 8)!}\\
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l.119 {\ex
\verb!I = identity_matrix(5)!} $5\times 5$-lik birim matris\\
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l.120 {\ex
\verb!J = jordan_block(-2,3)!}\\
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l.123 {\ex
\verb!var('x y z'); K = matrix(SR, [[x,y+z],[0,x^2*z]])!}\\
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l.126 {\ex
\verb!L=matrix(ZZ, 20, 80, {(5,9):30, (15,77):-6})!}\\
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| $\OT1/cmr/m/n/12 3 \OMS/cmsy/m/n/12 ^^B \OT1/cmr/m/n/12 3$-l^^?uk ma-tris, k^
^?o^^Xsegende $\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 2$, k^^?o^^Xsegen^^?ust^^?un
de $1$'ler blue[]\OT1/cmtt/m/n/12 var('x y z'); K = matrix(SR, [[x,y+z],[0,x^2*
z]])
[1]
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\verb!u = vector(QQ, [1,2,3])!},\quad{\ex\verb!v = vector(QQ, [1,2...
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l.133 ...\verb!u = vector(QQ, [1,2,3])!},\quad{\ex
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\verb!A = matrix(QQ, [[1,2,3],[4,5,6]])!}\\
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\verb!B = matrix(QQ, [[1,2],[3,4]])!}\\
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\verb!u*A!},\quad
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\verb!A*v!},\quad
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\verb!B*A!},\quad
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\verb!B^6!},\quad
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\verb!B^(-3)!}'nün tümü geçerlidir.\\
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l.143 {\ex
\verb!B.iterates(v, 6)!} $vB^0, vB^1,\dots, vB^5$'u üretir\\
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l.146 {\ex
\verb!f(x)=x^2+5*x+3!} tanımlıysa, {\ex\verb!f(B)!} geçerlidir\\
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l.146 ...\verb!f(x)=x^2+5*x+3!} tanımlıysa, {\ex
\verb!f(B)!} geçerlidir\\
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\verb!B.exp()!} $= e^B = \sum_{k=0}^{\infty}\frac{B^k}{k!}$
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\verb!M = MatrixSpace(QQ, 3, 4)!}\\
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\verb!A = M([1,2,3,4,5,6,7,8,9,10,11,12])!}\\
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\verb!M.basis()!} \verb!M!'nin tabanı \\
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\verb!M.dimension()!} \verb!M!'nin boyutu\\
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\verb!M.zero_matrix()!} \verb!M!'nin sıfır matrisi
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\verb!5*A+2*B!} doÄŸrusal bileÅŸim\\
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l.172 {\ex
\verb!A.inverse()!}, {\ex\verb!A^(-1)!}, {\ex\verb!~A!} = \verb!A!...
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l.172 {\ex\verb!A.inverse()!}, {\ex
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l.172 ...b!A.inverse()!}, {\ex\verb!A^(-1)!}, {\ex
\verb!~A!} = \verb!A!'nın...
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l.176 {\ex
\verb!A.transpose()!} $=\verb!A!^t=$ \verb!A!'nın devriği \\
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\verb!A.antitranspose()!} $\verb!A!^t$'nin satır ve sütunları t...
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l.180 {\ex
\verb!A.adjoint()!} Kofaktörler matrisi\\
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l.182 {\ex
\verb!A.conjugate()!} kutu kutu karmaşık eşlenikler\\
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\verb!A.restrict(V)!} \verb!A!'nın korunan \verb!V! altuzayına k...
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l.192 {\warn
Uyarı}: İlk satırın indisi 0'dır\\
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\verb!A.rescale_row(i,a)!} \verb!a*!(\verb!i! satırı)\\
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l.196 {\ex
\verb!A.add_multiple_of_row(i,j,a)!} \verb!a*!(\verb!j! satırı) ...
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l.198 {\ex
\verb!A.swap_rows(i,j)!} \verb!i! satırıyla \verb!j! satırı y...
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l.202 Yeni bir matris için, örn. \ {\ex
\verb!B = A.with_rescaled_row(i,a)!}
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l.207 {\ex
\verb!A.echelon_form()!},
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\verb!A.echelonize()!},
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\verb!A.hermite_form()!}\\
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l.211 {\warn
Uyarı}: Sonuçlar, tanım halkasına bağlıdır \\
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l.212 {\ex
\verb!A = matrix(ZZ,[[4,2,1],[6,3,2]])!}\\
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l.213 {\ex
\verb!B = matrix(QQ,[[4,2,1],[6,3,2]])!}\\
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\verb!A.echelon_form()!} & {\ex\verb!B.echelon_form()!}\\
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l.215 {\ex\verb!A.echelon_form()!} & {\ex
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l.228 {\ex
\verb!A.pivots()!} sütun uzayını geren sütunların indisleri\\
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l.229 {\ex
\verb!A.pivot_rows()!} satır uzayını geren satırların indisleri
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l.235 {\warn
Uyarı}: Satır ve sütunların isimlendirilmesi 0'dan başlar\\
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l.236 {\ex
\verb!A.nrows()!}\\
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l.237 {\ex
\verb!A.ncols()!}\\
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l.239 {\ex
\verb!A[i,j]!} \verb!i!-nci satır ve \verb!j!-nci sütundaki kutu...
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l.241 \skipin{\warn
Uyarı}: Doğru: \verb!A[2,3] = 8!, Yanlış: \verb!A[2]...
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l.243 {\ex
\verb!A[i]!} \verb!i! satırı (değiştirilemez bir Python destes...
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l.245 {\ex
\verb!A.row(i)!} \verb!i! satırı (Sage vektörü)\\
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l.247 {\ex
\verb!A.column(j)!} \verb!j! sütunu (Sage vektörü)\\
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l.249 {\ex
\verb!A.list()!} Matris, satır öncelikli dizilmiş (Python liste...
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l.250 {\ex
\verb!A.matrix_from_columns([8,2,8])!}\\
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\verb!A.matrix_from_rows([2,5,1])!}\\
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l.260 {\ex
\verb!A.rows()!} tüm satırlar (destelerden bir liste halinde)\\
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l.262 {\ex
\verb!A.columns()!} tüm sütunlar (destelerden bir liste halinde)\\
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l.263 {\ex
\verb!A.submatrix(i,j,nr,nc)!}\\
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l.267 {\ex
\verb!A[2:4,1:7]!}, {\ex\verb!A[0:8:2,3::-1]!} Python tarzı liste...
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l.267 {\ex\verb!A[2:4,1:7]!}, {\ex
\verb!A[0:8:2,3::-1]!} Python tarzı liste...
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l.273 {\ex
\verb!A.augment(B)!} $=[\verb!A|B!]$, \verb!A! matrisi \verb!B!'n...
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l.275 {\ex
\verb!A.stack(B)!} \verb!A! matrisi \verb!B!'nin üzerine konur\\
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l.277 {\ex
\verb!A.block_sum(B)!} \verb!A! solüstte, \verb!B! sağaltta blok...
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l.279 {\ex
\verb!A.tensor_product(B)!} \verb!B!'nin katları \verb!A!'ya uygu...
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l.284 {\ex
\verb!A.rank()!}\\
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l.285 {\ex
\verb!A.nullity() == A.left_nullity()!}\\
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l.286 {\ex
\verb!A.right_nullity()!}\\
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l.287 {\ex
\verb!A.determinant() == A.det()!}\\
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\verb!A.permanent()!}\\
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l.289 {\ex
\verb!A.trace()!}\\
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l.294 {\ex
\verb!A.norm() == A.norm(2)!} Öklid normu\\
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l.295 {\ex
\verb!A.norm(1)!} en büyük sütun toplamı\\
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l.296 {\ex
\verb!A.norm(Infinity)!} en büyük satır toplamı\\
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l.297 {\ex
\verb!A.norm('frob')!} Frobenius normu
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l.309 {\ex
\verb!.is_zero()!} (sıfır mı?),
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l.310 {\ex
\verb!.is_one()!} (birim matris mi?),\\
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\verb!.is_scalar()!} (birimin katı mı?),
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\verb!.is_square()!},\\
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\verb!.is_invertible()!},
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l.315 {\ex
\verb!.is_nilpotent()!}
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l.321 {\ex
\verb!A.charpoly('t')!} $=\det(\verb!t! - \verb!A!)$ (varsayılan ...
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l.322 {\ex
\verb! A.characteristic_polynomial() == A.charpoly()!}\\
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l.324 {\ex
\verb!A.fcp('t')!} çarpanlarına ayrılmış karakteristik polinom\\
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l.326 {\ex
\verb!A.minpoly()!} minimum polinom\\
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l.327 {\ex
\verb! A.minimal_polynomial() == A.minpoly()!}\\
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l.329 {\ex
\verb!A.eigenvalues()!} Özdeğerlerin listesi (sırasız, katlıl...
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l.337 {\ex
\verb!A.eigenvectors_left()!} vektörler solda (sağ $\to $\verb!_...
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l.349 {\ex
\verb!A.eigenmatrix_right()!} vektörler sağda \verb!_left! too\\
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l.359 {\warn
Önemli}: Bu yöntemler, uygun halkalarda tanımlıdır.\\
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l.366 {\ex
\verb!A.jordan_form(transformation=True)!}\\
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l.377 {\ex
\verb!A.smith_form()!} üç matris verir:\\
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l.388 {\ex
\verb!A.LU()!} üç matris verir:\\
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l.399 {\ex
\verb!A.QR()!} iki matris verir:\\
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l.410 {\ex
\verb!A.SVD()!} üç matris verir:\\
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l.416 {\ex
\verb!A.symplectic_form()!}\\
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l.417 {\ex
\verb!A.hessenberg_form()!}\\
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l.418 {\ex
\verb!A.cholesky()!}\par
[4]
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\verb!A.solve_right(B)!}, {\ex\verb!A.solve_left(B)!} sırasıyla ...
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l.427 {\ex\verb!A.solve_right(B)!}, {\ex
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l.429 {\ex
\verb!A = matrix(QQ, [[1,2],[3,4]])!}\\
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l.430 {\ex
\verb!b = vector(QQ, [3,4])!}\\
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l.431 ...için \verb!A*x = b!'nin çözümü {\ex
\verb!A\b!}$=\verb!A!^{-1}...
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l.431 ...x\verb!A\b!}$=\verb!A!^{-1}\verb!b!=${\ex
\verb!(-2, 5/2)!}'tir.
Overfull \hbox (11.95332pt too wide) in paragraph at lines 427--432
[]\OT1/cmr/m/n/12 blue[]\OT1/cmtt/m/n/12 A.solve_right(B)\OT1/cmr/m/n/12 , blue
[]\OT1/cmtt/m/n/12 A.solve_left(B) \OT1/cmr/m/n/12 s^^Pras^^Pyla []\OT1/cmtt/m/
n/12 A*X = B | \OT1/cmr/m/n/12 ve []\OT1/cmtt/m/n/12 X*A = B
! Undefined control sequence.
\ex ->\color
{blue}
l.444 {\ex
\verb!U = VectorSpace(QQ, 4)!} kesirler üstünde 4 boyutlu uzay\\
! Undefined control sequence.
\ex ->\color
{blue}
l.445 {\ex
\verb!V = VectorSpace(RR, 4)!} ``cisim'' 53-bit hassas gerçeller\\
! Undefined control sequence.
\ex ->\color
{blue}
l.446 {\ex
\verb!W = VectorSpace(RealField(200), 4)!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.448 {\ex
\verb!X = CC^4!} 4-boyutlu, 53-bit hassas karmaşıklar\\
! Undefined control sequence.
\ex ->\color
{blue}
l.449 {\ex
\verb!Y = VectorSpace(GF(7), 4)!} sonlu doÄŸrusal uzay\\
! Undefined control sequence.
\ex ->\color
{blue}
l.450 \skipin{\ex
\verb!Y.finite()!} sorusu Doğru (\verb!True!) yanıtı ver...
! Undefined control sequence.
\ex ->\color
{blue}
l.451 \skipin{\ex
\verb!len(Y.list())!} $=7^4=2401=$ \verb!Y!'nin üye sayısı
! Undefined control sequence.
\ex ->\color
{blue}
l.465 {\ex
\verb!V.dimension()!} \verb!V!'nin boyutu\\
! Undefined control sequence.
\ex ->\color
{blue}
l.466 {\ex
\verb!V.basis()!} \verb!V!'nin tabanı\\
! Undefined control sequence.
\ex ->\color
{blue}
l.467 {\ex
\verb!V.echelonized_basis()!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.468 {\ex
\verb!V.has_user_basis()!} kullanıcı \verb!V! için bir taban v...
! Undefined control sequence.
\ex ->\color
{blue}
l.469 {\ex
\verb!V.is_subspace(W)!} \verb!W!, \verb!V!'nin altuzayı mı?\\
! Undefined control sequence.
\ex ->\color
{blue}
l.470 {\ex
\verb!V.is_full()!} modül olarak, rank mertebeye eşit mi?\\
! Undefined control sequence.
\ex ->\color
{blue}
l.471 {\ex
\verb!Y = GF(7)^4!},\quad{\ex\verb!T = Y.subspaces(2)!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.471 {\ex\verb!Y = GF(7)^4!},\quad{\ex
\verb!T = Y.subspaces(2)!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.494 {\ex
\verb!span([v1,v2,v3], QQ)!} \verb!v1,v2,v3!'ün gerdiği altuzay...
! Undefined control sequence.
\ex ->\color
{blue}
l.499 {\ex
\verb!A.left_kernel() == A.kernel()!} sağ yan için \verb!right_!\\
! Undefined control sequence.
\ex ->\color
{blue}
l.500 {\ex
\verb!A.row_space() == A.row_module()!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.501 {\ex
\verb!A.column_space() == A.column_module()!}\\
! Undefined control sequence.
\ex ->\color
{blue}
l.502 {\ex
\verb!A.eigenspaces_right()!} vektörler sağda, sol için \verb!_...
[5]
! Undefined control sequence.
\ex ->\color
{blue}
l.506 {\ex
\verb!V.quotient(W)!} $= \verb!V!/ \verb!W! =$ \verb!V!'nin \verb...
! Undefined control sequence.
\ex ->\color
{blue}
l.507 {\ex
\verb!V.intersection(W)!} $= \verb!V! \cap \verb!W! =$ \verb!V!'ni...
! Undefined control sequence.
\ex ->\color
{blue}
l.508 {\ex
\verb!V.direct_sum(W)!} $= \verb!V! \oplus \verb!W! =$ \verb!V! il...
! Undefined control sequence.
\ex ->\color
{blue}
l.509 {\ex
\verb!V.subspace([v1,v2,v3])!} %% BURAYA
! Undefined control sequence.
\warn ->\bf \color
{red}
l.522 {\warn
Not:} Algoritmalar, nesnelerin temsil şekline göre değişir\\
! Undefined control sequence.
\ex ->\color
{blue}
l.526 {\ex
\verb!.is_dense()!} yoÄŸun mu?, {\ex\verb!.is_sparse()!} seyrek mi?\\
! Undefined control sequence.
\ex ->\color
{blue}
l.526 {\ex\verb!.is_dense()!} yoÄŸun mu?, {\ex
\verb!.is_sparse()!} seyrek mi?\\
! Undefined control sequence.
\ex ->\color
{blue}
l.527 {\ex
\verb!A.sparse_matrix()!} \verb!A!'nın seyrek temsili\\
! Undefined control sequence.
\ex ->\color
{blue}
l.528 {\ex
\verb!A.dense_rows()!} (yoğun) satır vektörleri olarak \verb!A!\\
! Undefined control sequence.
\warn ->\bf \color
{red}
l.557 {\warn
Not:} Farklı halkalar üzerinde farklı algoritmalar kullanıl...
! Undefined control sequence.
\ex ->\color
{blue}
l.558 {\ex
\verb!<nesne>.base_ring(R)!} vektör, matris gibi bir \verb!nesne! \\
! Undefined control sequence.
\ex ->\color
{blue}
l.560 {\ex
\verb!<nesne>.change_ring(R)!} vektör, matris gibi bir \verb!nesne!
! Undefined control sequence.
\ex ->\color
{blue}
l.562 {\ex
\verb!R.is_ring()!} halka mı? ,\quad{\ex\verb!R.is_field()!} cis...
! Undefined control sequence.
\ex ->\color
{blue}
l.562 ...\verb!R.is_ring()!} halka mı? ,\quad{\ex
\verb!R.is_field()!} cisi...
! Undefined control sequence.
\ex ->\color
{blue}
l.563 {\ex
\verb!R.is_integral_domain()!},\quad{\ex\verb!R.is_exact()!}
! Undefined control sequence.
\ex ->\color
{blue}
l.563 {\ex\verb!R.is_integral_domain()!},\quad{\ex
\verb!R.is_exact()!}
! Undefined control sequence.
\ex ->\color
{blue}
l.566 \skipin{\ex
\verb!ZZ!}\quad tamsayılar, halka\\
! Undefined control sequence.
\ex ->\color
{blue}
l.567 \skipin{\ex
\verb!QQ!}\quad kesir sayılar, cisim\\
! Undefined control sequence.
\ex ->\color
{blue}
l.568 \skipin{\ex
\verb!QQbar!}\quad cebirsel cisim, kayıpsız\\
! Undefined control sequence.
\ex ->\color
{blue}
l.569 \skipin{\ex
\verb!RDF!}\quad real double field, kayıpsız\\
! Undefined control sequence.
\ex ->\color
{blue}
l.570 \skipin{\ex
\verb!RR!}\quad 53-bit hassas gerçeller, kayıplı\\
! Undefined control sequence.
\ex ->\color
{blue}
l.571 \skipin{\ex
\verb!RealField(400)!}\quad 400-bit hassas gerçeller, kayÄ...
! Undefined control sequence.
\ex ->\color
{blue}
l.572 \skipin{\ex
\verb!CDF!,\quad\verb!CC!,\quad\verb!ComplexField(400)!}\qu...
! Undefined control sequence.
\ex ->\color
{blue}
l.573 \skipin{\ex
\verb!RIF!}\quad gerçel aralık cismi\\
! Undefined control sequence.
\ex ->\color
{blue}
l.574 \skipin{\ex
\verb!GF(2)!}\quad mod 2, cisim, özel algoritmalar\\
! Undefined control sequence.
\ex ->\color
{blue}
l.575 \skipin{\ex
\verb!GF(p) == FiniteField(p)!}\quad \verb!p! asal, sonlu c...
! Undefined control sequence.
\ex ->\color
{blue}
l.576 \skipin{\ex
\verb!Integers(6)!}\quad mod 6'da tamsayılar, yalnızca ha...
! Undefined control sequence.
\ex ->\color
{blue}
l.577 \skipin{\ex
\verb!CyclotomicField(7)!}\quad 1'in 7. kökleri eklenmiş ...
! Undefined control sequence.
\ex ->\color
{blue}
l.578 \skipin{\ex
\verb!QuadraticField(-5, 'x')!}\, kesirlere \verb!x=!$\sqrt...
! Undefined control sequence.
\ex ->\color
{blue}
l.579 \skipin{\ex
\verb!SR!}\quad simgesel ifadeler halkası
[6]
! LaTeX Error: \begin{document} on input line 48 ended by \end{multicols*}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.603 \end{multicols*}
[7] (./latex_196db71385b281e88596f68b95fb50851f88d04e_p.aux) )
(\end occurred inside a group at level 1)
### semi simple group (level 1) entered at line 48 (\begingroup)
### bottom level
(see the transcript file for additional information)
Output written on latex_196db71385b281e88596f68b95fb50851f88d04e_p.dvi (7 pages
, 18260 bytes).
Transcript written on latex_196db71385b281e88596f68b95fb50851f88d04e_p.log.
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