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