| Calling Sequence | Eigenvalues(A,eigenvects)
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| Parameters |
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| Return Type | list(numeric) | ||||||||||||
| Synopsis | Compute an eigenvalue/eigenvector decomposition of A. A must be a symmetric matrix. The function returns the vector containing the eigenvalues in increasing order. The optional second argument, if present must be a name that will be assigned with the matrix of the eigenvectors. The eigenvectors have norm 1 and are stored columnwise and the ith column corresponds to the ith eigenvalue. | ||||||||||||
| Examples | > A := [[3,1,2],[1,2,-1],[2,-1,5]]; A := [[3, 1, 2], [1, 2, -1], [2, -1, 5]] > alpha := Eigenvalues(A,V); alpha := [0.4921, 3.2444, 6.2635] > Vt := V^t; Vt := [[0.6041, -0.6782, -0.4185], [0.6191, 0.7301, -0.2894], [0.5018, -0.084230 29, 0.8609]] > A*Vt[1] = alpha[1]*Vt[1]; [0.2973, -0.3337, -0.2059] = [0.2973, -0.3337, -0.2059] > Vt[2]*Vt[2]; 1.0000 | ||||||||||||
| See also | Cholesky, convolve, GaussElim, GivensElim, Identity, matrix, matrix_inverse, SvdAnalysis, transpose | ||||||||||||