Linear Algebra
~~~~~~~~~~~~~~


+ `aff2ab`_ linear (affine) function to A,b conversion
+ `balanc`_ matrix or pencil balancing
+ `bdiag`_ block diagonalization, generalized eigenvectors
+ `chol`_ Cholesky factorization
+ `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 factorization with pivoting
+ `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


.. _expm: expm.html
.. _givens: givens.html
.. _gspec: gspec.html
.. _cmb_lin: cmb_lin.html
.. _nlev: nlev.html
.. _trace: trace.html
.. _rankqr: rankqr.html
.. _schur: schur.html
.. _sva: sva.html
.. _psmall: psmall.html
.. _det: det.html
.. _inv: inv.html
.. _balanc: balanc.html
.. _projspec: projspec.html
.. _coff: coff.html
.. _rowshuff: rowshuff.html
.. _rcond: rcond.html
.. _rref: rref.html
.. _fullrf: fullrf.html
.. _gschur: gschur.html
.. _qr: qr.html
.. _squeeze: squeeze.html
.. _kroneck: kroneck.html
.. _range: range.html
.. _spec: spec.html
.. _fstair: fstair.html
.. _linsolve: linsolve.html
.. _glever: glever.html
.. _svd: svd.html
.. _chol: chol.html
.. _cond: cond.html
.. _sylv: sylv.html
.. _quaskro: quaskro.html
.. _spanplus: spanplus.html
.. _fullrfk: fullrfk.html
.. _orth: orth.html
.. _im_inv: im_inv.html
.. _bdiag: bdiag.html
.. _randpencil: randpencil.html
.. _classmarkov: classmarkov.html
.. _rank: rank.html
.. _lsq: lsq.html
.. _lyap: lyap.html
.. _proj: proj.html
.. _ereduc: ereduc.html
.. _genmarkov: genmarkov.html
.. _rowcomp: rowcomp.html
.. _householder: householder.html
.. _eigenmarkov: eigenmarkov.html
.. _pbig: pbig.html
.. _colcomp: colcomp.html
.. _companion: companion.html
.. _polar: polar.html
.. _pencan: pencan.html
.. _kernel: kernel.html
.. _penlaur: penlaur.html
.. _spaninter: spaninter.html
.. _lu: lu.html
.. _sqroot: sqroot.html
.. _spantwo: spantwo.html
.. _hess: hess.html
.. _aff2ab: aff2ab.html
.. _pinv: pinv.html