Linear Algebra

• Eigenvalue and Singular Value
  • balanc — matrix or pencil balancing
  • bdiag — block diagonalization, generalized eigenvectors
  • hess — Hessenberg form
  • pbig — eigen-projection
  • projspec — spectral operators
  • psmall — spectral projection
  • schur — [ordered] Schur decomposition of matrix and pencils
  • spec — eigenvalues of matrices and pencils
  • sva — singular value approximation
  • svd — singular value decomposition
• Factorization
  • givens — Givens transformation
  • householder — Householder orthogonal reflexion matrix. Symetrical wrt a plane
  • sqroot — W*W' hermitian factorization
• Kernel
  • colcomp — column compression, kernel, nullspace
  • fullrf — full rank factorization
  • fullrfk — full rank factorization of A^k
  • 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
  • chol — Cholesky factorization
  • inv — matrix inverse
  • linsolve — linear equation solver
  • lsq — linear least square problems.
  • lu — LU factorization with pivoting
  • pinv — pseudoinverse
  • qr — QR decomposition
  • rankqr — rank revealing QR factorization
• 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
  • 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
  • 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
• proj — projection