Linear Algebra and Analytic Geometry for Physical Sciences by Giovanni Landi & Alessandro Zampini

Author:Giovanni Landi & Alessandro Zampini
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

is then orthogonal by construction. We notice that P can be always chosen to be an element in , since a permutation of its columns changes the sign of its determinant, and is compatible with the permutation of the eigenvalue in the diagonal matrix.

In order to explicitly compute the matrix P we see that the eigenspace for any is given by the solutions of the linear homogeneous system associated to the matrix

Since we already know that , such a linear system is equivalent to a single linear equation. We can write

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