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Chapter 5: Eigenvalues and Eigenvectors
https://doi.org/10.1142/9789813143807_0005Cited by:0 (Source: Crossref)
Abstract:
Let A be an n×n matrix over ℂ. The complex number λ is called an eigenvalue of A if and only if the matrix (A − λIn) is singular. Let x be a nonzero column vector in ℂn. Then x is called an eigenvector belonging to (or associated with) the eigenvalue λ if and only if (A − λIn)x = 0. The equation
Ax=λx
is called the eigenvalue equation. For an eigenvector x of A, Ax is a scalar multiple of x. The eigenvalues are found from the characteristic equation det(A − λIn) = 0.
