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Linear equations, eigenvalues, singular values, decomposition,
matrix operations, matrix structure

Linear algebra functions in MATLAB^{®} provide fast, numerically
robust matrix calculations. Capabilities include a variety of matrix
factorizations, linear equation solving, computation of eigenvalues
or singular values, and more. For an introduction, see Matrices in the MATLAB Environment.

**Matrices in the MATLAB Environment**

Matrix creation and basic operations.

Solve several types of systems of linear equations.

Eigenvalue and eigenvector computation.

Singular value decomposition (SVD).

Common matrix factorizations (Cholesky, LU, QR).

This example shows 3 of the 19 ways to compute the exponential of a matrix.

**Determine Whether Matrix Is Symmetric Positive Definite**

Use `chol`

and `eig`

to determine whether a matrix is symmetric positive definite (a symmetric matrix with all positive eigenvalues).

LAPACK provides a foundation of routines for linear algebra functions and matrix computations in MATLAB.