Some properties

Linear Algebra and the C Language · Wikibooks

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    From Wikibooks, under CC BY-SA 4.0, as the source states it. This page at Wikibooks.


    In linear algebra, an eigenvector is a vector that has its direction unchanged (or reversed) by a given linear transformation ... Wikipedia: Eigenvectors

    Some properties:

    The sum of the eigenvalues ​​of A is equal to the trace of A:

    The product of the eigenvalues ​​of A is equal to the determinant of A:

    The eigenvalues ​​of the inverse of A correspond to the inverses of the eigenvalues ​​of A:

    The eigenvalues ​​of sA correspond to the eigenvalues ​​of A multiplied by s:

    The eigenvalues ​​of A+sID correspond to the eigenvalues ​​of A plus s:

    The eigenvalues ​​of A**P correspond to the eigenvalues ​​of A to the power of P:

    Similar matrices have the same eigenvalues.

    The eignvectors form an orthonormal basis:

    We know that: A V = λ V. If λ = 0 with A and V different from zero, verify if A V = 0.

    We know that: A V = λ V. If λ = 0 with A and V different from zero, verify if A V = 0.