Linear Algebra and the C Language/a0dh
In linear algebra, an eigenvector is a vector that has its direction unchanged (or reversed) by a given linear transformation ... Wikipedia: Eigenvectors
Some properties:
[edit | edit source]The sum of the eigenvalues of A is equal to the trace of A:
- Random values ... ... ... ... ... Octave
The product of the eigenvalues of A is equal to the determinant of A:
- Random values ... ... ... ... ... Octave
The eigenvalues of the inverse of A correspond to the inverses of the eigenvalues of A:
- Random values ... ... ... ... ... Octave
The eigenvalues of sA correspond to the eigenvalues of A multiplied by s:
- Random values ... ... ... ... ... Octave
The eigenvalues of A+sID correspond to the eigenvalues of A plus s:
- Random values ... ... ... ... ... Octave
The eigenvalues of A**P correspond to the eigenvalues of A to the power of P:
- Random values ... ... ... ... ... Octave
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.