Linear Algebra with Applications, 10th Edition

MATLAB Functions

To compute the eigenvalues of a square matrix A, we need only type eig(A). The eigenvectors and eigenvalues can be computed by setting

$$\left[\begin{array}{cc}X& D\end{array}\right]=\mathsf{\text{eig}}\left(A\right)$$

Similarly, we can compute the determinant, inverse, condition number, norm, and rank of a matrix with simple one-word commands. Matrix factorizations such as the LU, QR, Cholesky, Schur decomposition, and singular value decomposition can be computed with a single command. For example, the command

$$\left[\begin{array}{cc}Q& R\end{array}\right]=\mathsf{\text{qr}}\left(A\right)$$

will produce an orthogonal (or unitary) matrix Q and an upper triangular matrix R, with the same dimensions as A, such that $A=QR$.