What are the functions of the ‘inv’ function in MATLAB?

In Matlab, the inv function serves several functions:

1. Calculate the inverse of a matrix: inv(A) can calculate the inverse matrix of matrix A, if it exists. The inverse matrix satisfies A * inv(A) = inv(A) * A = I, where I is the identity matrix.
2. Solving a system of linear equations: inv(A) * b can be used to solve the linear equation Ax = b, where A is the coefficient matrix, b is the constant vector, and x is the unknown vector.
3. Compute the pseudoinverse matrix: When a matrix A is not invertible, the inv(A) function will return the pseudoinverse matrix of A. The pseudoinverse matrix is a matrix that satisfies AA+ = A+ A = I, where A+ is the pseudoinverse of matrix A.

It is important to note that when matrix A is not invertible, the inv(A) function will generate a warning and return an approximate pseudo-inverse matrix. Therefore, in practical applications, one should use the inv function cautiously and employ other more suitable methods to solve linear equations or pseudo-inverse matrices.