Scilab Online Help
2023.1.0 - English

Linear Algebra

• Eigenvalue and Singular Value
  • balanc — matrix or pencil balancing
  • bdiag — block diagonalization, generalized eigenvectors
  • eigs — calculates largest eigenvalues and eigenvectors of matrices
  • pbig — eigen-projection
  • projspec — spectral operators
  • psmall — spectral projection
  • spec — eigenvalues, and eigenvectors of a matrix or a pencil
  • sva — singular value approximation
  • svd — singular value decomposition
• Factorization
  • chol — Cholesky factorization
  • fullrf — full rank factorization
  • fullrfk — full rank factorization of A^k
  • hess — Hessenberg form
  • lu — LU factorization with pivoting
  • polar — polar decomposition of a square matrix
  • qr — QR decomposition
  • rankqr — rank revealing QR factorization
  • schur — [ordered] Schur decomposition of matrix and pencils
  • sqroot — W*W' hermitian factorization
• Kernel
  • colcomp — column compression, kernel, nullspace
  • im_inv — inverse image
  • kernel — kernel, null space
  • range — range (span) of A^k
  • rowcomp — row compression, range
• Linear Equations
  • aff2ab — linear (affine) function to A,b conversion
  • inv — matrix inverse
  • linsolve — linear equation solver
  • lsq — linear least square solution of A*X=B with minimal norm(X)
  • pinv — pseudoinverse
• Markov Matrices
  • classmarkov — recurrent and transient classes of Markov matrix
  • eigenmarkov — normalized left and right Markov eigenvectors
  • genmarkov — generates random markov matrix with recurrent and transient classes
• Matrix Analysis
  • cond — condition number of a matrix
  • det — determinant of a square matrix
  • orth — orthogonal basis
  • rank — rank
  • rcond — inverse condition number
  • rref — computes matrix row echelon form by lu transformations
  • trace — trace
• Matrix Pencil
  • companion — companion matrix
  • ereduc — computes matrix column echelon form by qz transformations
  • fstair — computes pencil column echelon form by qz transformations
  • glever — inverse of matrix pencil
  • kroneck — Kronecker form of matrix pencil
  • lyap — Lyapunov equation
  • pen2ea — pencil to E,A conversion
  • pencan — canonical form of matrix pencil
  • penlaur — Laurent coefficients of matrix pencil
  • quaskro — quasi-Kronecker form
  • randpencil — random pencil
  • rowshuff — shuffle algorithm
• State-Space Matrices
  • coff — resolvent (cofactor method)
  • nlev — Leverrier's algorithm
• Subspaces
  • spaninter — subspace intersection
  • spanplus — sum of subspaces
  • spantwo — sum and intersection of subspaces
• givens — Givens transformation
• householder — Householder orthogonal reflexion matrix. Symetrical wrt a plane
• proj — projection

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