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Linear Algebra

  • aff2ab linear (affine) function to A,b conversion
  • balanc matrix or pencil balancing
  • bdiag block diagonalization, generalized eigenvectors
  • chfact sparse Cholesky factorization
  • chol Cholesky factorization
  • chsolve sparse Cholesky solver
  • coff resolvent (cofactor method)
  • colcomp column compression, kernel, nullspace
  • companion companion matrix
  • cond condition number
  • det determinant
  • ereduc computes matrix column echelon form by qz transformations
  • exp element-wise exponential
  • expm square matrix exponential
  • fstair computes pencil column echelon form by qz transformations
  • fullrf full rank factorization
  • fullrfk full rank factorization of A^k
  • givens Givens transformation
  • glever inverse of matrix pencil
  • gschur generalized Schur form (matrix pencils).
  • gspec eigenvalues of matrix pencil
  • hess Hessenberg form
  • householder Householder orthogonal reflexion matrix
  • im_inv inverse image
  • inv matrix inverse
  • kernel kernel, nullspace
  • kroneck Kronecker form of matrix pencil
  • linsolve linear equation solver
  • lu LU factors of Gaussian elimination
  • ludel utility function used with lufact
  • lufact sparse lu factorization
  • luget sparse lu factorization
  • lusolve sparse linear system solver
  • lyap Lyapunov equation
  • nlev Leverrier's algorithm
  • orth orthogonal basis
  • pbig eigen-projection
  • pencan canonical form of matrix pencil
  • penlaur Laurent coefficients of matrix pencil
  • pinv pseudoinverse
  • polar polar form
  • proj projection
  • projspec spectral operators
  • psmall spectral projection
  • qr QR decomposition
  • quaskro quasi-Kronecker form
  • randpencil random pencil
  • range range (span) of A^k
  • rank rank
  • rcond inverse condition number
  • rowcomp row compression, range
  • rowshuff shuffle algorithm
  • rref computes matrix row echelon form by lu transformations
  • schur [ordered] Schur decomposition
  • spaninter subspace intersection
  • spanplus sum of subspaces
  • spantwo sum and intersection of subspaces
  • spchol sparse cholesky factorization
  • spec eigenvalues
  • sqroot W*W' hermitian factorization
  • sva singular value approximation
  • svd singular value decomposition
  • sylv Sylvester equation.
  • trace trace