## Matrix Calculator applet

The matrix calculator below computes inverses, eigenvalues and eigenvectors of 2 x 2, 3 x 3, 4 x 4 and 5 x 5 matrices, multiplies a matrix and a vector, and solves the matrix-vector equation Ax = b. You can change the entries in the matrix A and vector b by clicking on them and typing.
• Press the Invert button to see A-1. This requires the matrix to be nonsingular.
• Press the Eigen button to see the eigenvalues, with an eigenvector below each eigenvalue. Note that in the case of complex eigenvalues, only one of each complex-conjugate pair is shown.
• Press the Solve button to see the solution of Ax=b. This requires the matrix to be nonsingular.
• Press the Multiply button to see the product Ab.
• You can keep three different matrices A, B, C and three different vectors a, b and c. To switch among them, click on the name and choose another one. The buttons always operate on the currently-chosen matrix and vector.
• The Copy button copies the latest result (if any) into the currently shown matrix or vector.
• An inverse matrix will be copied into the current matrix.
• For the result of Eigen, the three eigenvectors are copied into the columns of the current matrix. In the case of complex eigenvalues, the real part of a complex eigenvector is copied into one column and the imaginary part into the next column.
• For the result of Solve, the solution vector is copied into the current vector.
• Click on 5 x 5 to change the matrix and vector sizes. Note that this sets all entries of the matrices and vectors to 0.

This applet uses the JAMA linear algebra package.