# Linear Algebra

You can use the LabWindows/CVI Advanced Analysis Library to perform matrix computation and analysis, including solving eigenvalue and eigenvector problems, solving systems of linear equations, and factoring matrices.

The LabWindows/CVI Advanced Analysis Library includes the following linear algebra functions:

Function | Description
--- | ---
BackSub | Solves the linear equations a * x = y by backward substitution.
CheckPosDef | Checks the positive definiteness of the real square input matrix.
Cholesky | Calculates the Cholesky factorization of a real, symmetric positive definite input matrix.
ConditionNumber | Calculates the condition number of a real input matrix.
CxCheckPosDef | Checks the symmetry and positive definiteness of a complex, square matrix.
CxCholesky | Calculates the Cholesky factorization of a complex, symmetric positive definite input matrix.
CxConditionNumber | Calculates the condition number of a complex input matrix.
CxDeterminant | Computes the determinant of a complex matrix.
CxDotProduct | Compute the dot product of complex vectors.
CxEigenValueVector | Calculates the eigenvalues and the corresponding eigenvectors of a complex, square input matrix.
CxEigenVBack | Transforms the complex eigenvectors of a balanced matrix to those of the original matrix.
CxGenEigenAB | Computes the generalized eigenvalues and, optionally, the left and/or right generalized eigenvectors for a pair of complex matrices.
CxGenInvMatrix | Calculates the inverse of the real, square input matrix.
CxHess | Calculates the Hessenberg decomposition for a complex matrix.
CxLU | Performs an LU decomposition on a complex, square matrix.
CxMatrixBalance | Balances a general complex matrix so that its eigenvectors can be computed more accurately.
CxMatrixMul | Multiples two complex matrices.
CxMatrixNorm | Computes the norm of a complex matrix.
CxMatrixRank | Computes the rank of a complex matrix.
CxOuterProduct | Computes the outer product of two complex vectors.
CxPseudoInverse | Computes the pseudoinverse of a complex matrix.
CxQR | Calculates the QR factorization of the complex input matrix.
CxQREx | Performs the QR factorization for a complex matrix.
CxQZ | Performs the QZ decomposition of a pair of complex matrices.
CxSchur | Performs the Schur decomposition of a complex matrix.
CxSolveEqs | Solves complex linear equations of the format AX = B.
CxSpecialMatrix | Generates a special type of complex matrix.
CxSVD | Calculates the Singular Value Decomposition (SVD) factorization of the complex input matrix.
CxSVDEx | Calculates the Singular Value Decomposition (SVD) factorization for a complex matrix.
CxSVDS | Calculates only the singular values that result from the Singular Value Decomposition (SVD) factorization of the complex input matrix.
CxTrace | Computes the trace of a complex matrix.
CxTranspose | Computes the conjugate transpose of a complex matrix.
Determinant | Computes the determinant of a real matrix.
DotProduct | Computes the dot product of real vectors.
EigenVBack | Transforms the eigenvectors of a balanced matrix to those of the original matrix.
ForwSub | Solves the linear equations a * x = y by forward substitution.
GenDeterminant | Calculates the determinant of a real, square input matrix.
GenEigenAB | Computes the generalized eigenvalues and, optionally, the left and/or right generalized eigenvectors for a pair of real matrices.
GenEigenValueVector | Calculates the eigenvalues and the corresponding eigenvectors of a real, square input matrix.
GenInvMatrix | Calculates the inverse of the real, square input matrix of the type you specify.
Hess | Performs a Hessenberg decomposition of a real matrix.
InvMatrix | Finds the inverse matrix of a square matrix.
LU | Performs an LU matrix decomposition.
MatrixBalance | Balances a general matrix so that its eigenvectors can be computed more accurately.
MatrixMul | Multiples two real matrices.
MatrixNorm | Calculates the norm of a real input matrix.
MatrixRank | Calculates the rank of the real input matrix.
OuterProduct | Calculates the outer product of the real input vectors.
PseudoInverse | Calculates the generalized inverse of the real input matrix.
QREx | Calculates the QR factorization for a real matrix.
QZ | Performs the QZ decomposition of a pair of real matrices.
Schur | Computes the Schur decomposition of a real matrix.
SolveEqs | Solves real linear equations as follows: AX = B.
SpecialMatrix | Generates one of the following special types of real matrix: Identity, Diagonal, Toeplitz, Vandermonde, and Companion.
SVDEx | Computes the singular value decomposition (SVD) of a real matrix.
SymEigenValueVector | Calculates the eigenvalues and the corresponding eigenvectors of a real, symmetric square input matrix.
Trace | Finds the trace of the 2D input matrix.
Transpose | Computes the transpose of a real matrix.