Linear Algebra


Table of Contents

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
classmarkov — recurrent and transient classes of Markov matrix
cmb_lin — symbolic linear combination
coff — resolvent (cofactor method)
colcomp — column compression, kernel, nullspace
companion — companion matrix
cond — condition number
det — determinant
eigenmarkov — normalized left and right Markov eigenvectors
ereduc — computes matrix column echelon form by qz transformations
expm — square matrix exponential
fstair — computes pencil column echelon form by qz transformations
fullrf — full rank factorization
fullrfk — full rank factorization of A^k
genmarkov — generates random markov matrix with recurrent and transient classes
givens — Givens transformation
glever — inverse of matrix pencil
gschur — generalized Schur form (obsolete).
gspec — eigenvalues of matrix pencil (obsolete)
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
lsq — linear least square problems.
lu — LU factors of Gaussian elimination
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
rankqr — rank revealing QR factorization
rcond — inverse condition number
rowcomp — row compression, range
rowshuff — shuffle algorithm
rref — computes matrix row echelon form by lu transformations
schur — [ordered] Schur decomposition of matrix and pencils
spaninter — subspace intersection
spanplus — sum of subspaces
spantwo — sum and intersection of subspaces
spec — eigenvalues of matrices and pencils
sqroot — W*W' hermitian factorization
squeeze — squeeze
sva — singular value approximation
svd — singular value decomposition
sylv — Sylvester equation.
trace — trace