### Linear Algebra

• Eigenvalue and Singular Value
• balancmatrix or pencil balancing
• bdiagblock diagonalization, generalized eigenvectors
• eigscalculates largest eigenvalues and eigenvectors of matrices
• pbigeigen-projection
• projspecspectral operators
• psmallspectral projection
• speceigenvalues, and eigenvectors of a matrix or a pencil
• svasingular value approximation
• svdsingular value decomposition
• Factorization
• cholCholesky factorization
• fullrffull rank factorization
• fullrfkfull rank factorization of A^k
• hessHessenberg form
• luLU factorization with pivoting
• polarpolar decomposition of a square matrix
• qrQR decomposition
• rankqrrank revealing QR factorization
• schur[ordered] Schur decomposition of matrix and pencils
• sqrootW*W' hermitian factorization
• Kernel
• colcompcolumn compression, kernel, nullspace
• im_invinverse image
• kernelkernel, null space
• rangerange (span) of A^k
• rowcomprow compression, range
• Linear Equations
• aff2ablinear (affine) function to A,b conversion
• invmatrix inverse
• linsolvelinear equation solver
• lsqlinear least square solution of A*X=B with minimal norm(X)
• pinvpseudoinverse
• Markov Matrices
• classmarkovrecurrent and transient classes of Markov matrix
• eigenmarkovnormalized left and right Markov eigenvectors
• genmarkovgenerates random markov matrix with recurrent and transient classes
• Matrix Analysis
• condcondition number of a matrix
• detdeterminant of a square matrix
• orthorthogonal basis
• rankrank
• rcondinverse condition number
• rrefcomputes matrix row echelon form by lu transformations
• tracetrace
• Matrix Pencil
• companioncompanion matrix
• ereduccomputes matrix column echelon form by qz transformations
• fstaircomputes pencil column echelon form by qz transformations
• gleverinverse of matrix pencil
• kroneckKronecker form of matrix pencil
• lyapLyapunov equation
• pen2eapencil to E,A conversion
• pencancanonical form of matrix pencil
• penlaurLaurent coefficients of matrix pencil