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Section 22.2 Terminology and notation
- similar matrices
a pair of square matrices \(A\) and \(B\) for which there exists an invertible matrix \(P\) satisfying \(B=\inv{P}AP\)
- transition matrix
an invertible matrix \(P\) that realizes a similarity relationship \(B=\inv{P}AP\) for similar matrices \(A\) and \(B\)
- diagonalizable
a square matrix that is similar to a diagonal matrix
The next two definitions apply to an eigenvalue of a square matrix.
- algebraic multiplicity
the number of times the eigenvalue is repeated as a root of the characteristic polynomial of the matrix
- geometric multiplicity
the dimension of the corresponding eigenspace
