MatricesLibrary of functions operating on matrices 
Examples demonstrating the usage of the Math.Matrices functions 

Convert a matrix into its string representation 

Compare whether two Real matrices are identical 

Solve real system of linear equations A*x=b with a b vector (Gaussian elimination with partial pivoting) 

Solve real system of linear equations A*X=B with a B matrix (Gaussian elimination with partial pivoting) 

Solve linear equation A*x = b (exactly if possible, or otherwise in a least square sense; A may be nonsquare and may be rank deficient) 

Solve linear equation A*X = B (exactly if possible, or otherwise in a least square sense; A may be nonsquare and may be rank deficient) 

Solve a linear equality constrained least squares problem 

LU decomposition of square or rectangular matrix 

Solve real system of linear equations P*L*U*x=b with a b vector and an LU decomposition (from LU(..)) 

Solve real system of linear equations P*L*U*X=B with a B matrix and an LU decomposition (from LU(..)) 

Return eigenvalues and eigenvectors for a real, nonsymmetric matrix in a Real representation 

Return real valued block diagonal matrix J of eigenvalues of matrix A (A=V*J*Vinv) 

Return singular values and left and right singular vectors 

Return the QR decomposition of a square matrix with optional column pivoting (A(:,p) = Q*R) 

Return upper Hessenberg form of a matrix 

Return the real Schur form (rsf) S of a square matrix A, A=QZ*S*QZ' 

Return the Cholesky factorization of a symmetric positive definite matrix 

Return a balanced form of matrix A to improve the condition of A 

Return a balanced form of a system [A,B;C,0] to improve its condition by a state transformation 

Return the trace of matrix A, i.e., the sum of the diagonal elements 

Return determinant of a matrix (computed by LU decomposition; try to avoid det(..)) 

Return inverse of a matrix (try to avoid inv(..)) 

Return rank of a rectangular matrix (computed with singular values) 

Return the condition number norm(A)*norm(inv(A)) of a matrix A 

Return the reciprocal condition number of a matrix 

Return the pnorm of a matrix 

Return the Frobenius norm of a matrix 

Return the orthonormal nullspace of a matrix 

Return the exponential of a matrix by adaptive Taylor series expansion with scaling and balancing 

Return the exponential and the integral of the exponential of a matrix 

Return the exponential, the integral of the exponential, and timeweighted integral of the exponential of a matrix 

Return solution X of the continuoustime Lyapunov equation X*A + A'*X = C 

Return solution X of the continuoustime Sylvester equation A*X + X*B = C 

Return solution X of the continuoustime algebraic Riccati equation A'*X + X*A  X*B*inv(R)*B'*X + Q = 0 (care) 

Return solution X of the discretetime Lyapunov equation A'*X*A + sgn*X = C 

Return solution of the discretetime Sylvester equation A*X*B + sgn*X = C 

Return solution of discretetime algebraic Riccati equation A'*X*A  X  A'*X*B*inv(R + B'*X*B)*B'*X*A + Q = 0 (dare) 

Sort the rows or columns of a matrix in ascending or descending order 

Flip the columns of a matrix in left/right direction 

Flip the rows of a matrix in up/down direction 

Interface to LAPACK library (should usually not directly be used but only indirectly via Modelica.Math.Matrices) 

Utility functions that should not be directly utilized by the user 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This library provides functions operating on matrices. Below, the functions are ordered according to categories and a typical call of the respective function is shown. Most functions are solely an interface to the external LAPACK library.
Note: A' is a short hand notation of transpose(A):
Basic Information
Linear Equations
Matrix Factorizations
Matrix Properties
Matrix Exponentials
Matrix Equations
Matrix Manipulation