Background: If a square matrix (A), a number (λ), and a vector (v) are related by the equation Av = λv, then λ and v are said to be an eigenvalue and eigenvector respectively of A. An n x n matrix that is symmetric (like most of significance and like the example below) has n eigenvalues, each corresponding to an eigenvector that points in a direction perpendicular to the other (n - 1) eigenvectors. Many calculations involving a matrix can be done easily - if at all - only after first calculating its eigenvectors and eigenvalues, a process often called diagonalization. This API diagonalizes matrices using the Jacobi method.

Instructions: After the url above you should type / followed by a comma-separated list of the column vectors, none of which includes elements in the lower-triangular portion of the matrix. Each column vector is a parenthesis-wrapped comma-separated list of numbers. If you want the results in json instead of html, snuggle /api immediately after ...heroku.com

Example: The matrix depicted below is specified for this API by the url ...heroku.com/(1),(2,3),(4,5,6)
Note that the last number (1, 3, or 6) in each column vector is along the matrix's diagonal.

1.0	2.0	4.0
2.0	3.0	5.0
4.0	5.0	6.0

The eigenvalues for this particular matrix are approximately -0.057, -1.507, and 11.564.

Here are some unrelated webpages that also calculate eigenvalues and eigenvectors: