A 2×2 matrix:

Create a function for solving the matrix equation :

Find the solution of for :

Find the solution of for a matrix :

Do computations using exact arithmetic:

Do computations using machine‐number arithmetic:

Do computations using 24‐digit arithmetic:

Get a factorization for a large sparse matrix:

Show the solution of :

Find the eigenvector associated with the smallest eigenvalue:

Approximate value of the eigenvalue:

Expressions for a finite difference approximation to the Laplacian in 2 dimensions:

A matrix approximating the Laplacian operator:

A linear solve function for the matrix:

An approximate solution for the Poisson equation on the unit rectangle:

An approximate solution for the Poisson equation on the unit rectangle:

A LinearSolveFunction is effectively like a matrix inverse. A large sparse matrix:

Time to compute and memory used by the linear solve function:

Time to compute and memory used by the inverse matrix:

Comparison of f and the inverse matrix for a random vector b:

Create a LinearSolveFunction for a simple matrix:

Compute the inverse matrix from f:

Compute the inverse matrix using Inverse:

Matrix factorizations are not found for rectangular matrices:

A solution is found: