# Linear Algebra

DSP System Toolbox™ system linear algebra blocks enable you to work with
matrices in Simulink^{®}. For example, to solve a set of linear equations through
Levinson-Durbin and Cholesky methods, use the Levinson-Durbin and Cholesky Solver blocks. These
techniques are commonly used in applications such as the Yule-Walker AR
problem and linear predictive coding. To factorize a square matrix into
upper and lower components, use methods such as LDL factorization and
the LU factorization. To invert matrices, use methods such as Cholesky
factorization, LDL factorization, and LU factorization. For a summary of
all the supported techniques and the corresponding blocks in DSP System Toolbox which implement the techniques, see Linear Algebra and Least Squares.

## Blocks

## Topics

**Linear Algebra and Least Squares**Solve systems of linear equations.

**LDL Factorization of 3-by-3 Hermitian Positive Definite Matrix**Simulink model example that shows how to use the LDL Factorization block.

**Solve Matrix Equation Using Backward Substitution**Use Backward Substitution block to solve a system of linear equations. Verify the solution using Matrix Multiply block.

**Solve Matrix Equation Using Forward Substitution**Use Forward Substitution block to solve a system of linear equations. Verify the solution using Matrix Multiply block.

**Find Inverse of Matrix Using the LU Inverse Block**Find inverse of a square matrix using the LU Inverse block.

**Solve Matrix Equation Using LU Solver**Use LU Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.

**Solve Matrix Equation Using Singular Value Decomposition**Use SVD Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.

**Solve Matrix Equation Using Cholesky Solver**Use Cholesky Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.

**Factorize Matrix Using LU Factorization Block**Factorize a matrix using the LU Factorization block.