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2023.0.0 - Русский


Linear Algebra

  • eigen
    • balancmatrix or pencil balancing
    • bdiagблоковая диагонализация, обобщённые собственные векторы
    • eigscalculates largest eigenvalues and eigenvectors of matrices
    • pbigeigen-projection
    • projspecspectral operators
    • psmallspectral projection
    • specсобственные значения и собственные вектора матрицы или пучка
    • svasingular value approximation
    • svdsingular value decomposition
  • linear
    • aff2ablinear (affine) function to A,b conversion
    • invmatrix inverse
    • linsolvelinear equation solver
    • lsqлинейное решение наименьших квадратов A*X=B с минимальной norm(X)
    • pinvpseudoinverse
  • matrix
    • condcondition number of a matrix
    • detопределитель квадратной матрицы
    • orthorthogonal basis
    • rankrank
    • rcondinverse condition number
    • rrefcomputes matrix row echelon form by lu transformations
    • tracetrace
  • pencil
    • companioncompanion matrix
    • ereduccomputes matrix column echelon form by qz transformations
    • fstaircomputes pencil column echelon form by qz transformations
    • gleverinverse of matrix pencil
    • kroneckKronecker form of matrix pencil
    • lyapLyapunov equation
    • pen2eaпреобразование пучка матриц в E, A
    • pencancanonical form of matrix pencil
    • penlaurLaurent coefficients of matrix pencil
    • quaskroquasi-Kronecker form
    • randpencilrandom pencil
    • rowshuffshuffle algorithm
  • Factorization
    • cholCholesky factorization
    • fullrffull rank factorization
    • fullrfkfull rank factorization of A^k
    • hessHessenberg form
    • luLU factorization with pivoting
    • qrQR decomposition
    • rankqrrank revealing QR factorization
    • schur[ordered] Schur decomposition of matrix and pencils
    • sqrootW*W' hermitian factorization
  • Kernel
    • colcompcolumn compression, kernel, nullspace
    • im_invinverse image
    • kernelkernel, null space
    • rangerange (span) of A^k
    • rowcomprow compression, range
  • Markov Matrices
    • classmarkovrecurrent and transient classes of Markov matrix
    • eigenmarkovnormalized left and right Markov eigenvectors
    • genmarkovgenerates random markov matrix with recurrent and transient classes
  • State-Space Matrices
    • coffresolvent (cofactor method)
    • nlevLeverrier's algorithm
  • Subspaces
  • givensGivens transformation
  • householderHouseholder orthogonal reflexion matrix. Symetrical wrt a plane
  • projprojection
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