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Section 25.2 Terminology and notation
similar matrices
a pair of square matrices
\(A \) and
\(B \) for which there exists an invertible matrix
\(P \) satisfying
\(B = \inv{P} A P \)
transition matrix
an invertible matrix
\(P \) that realizes a similarity relationship
\(B = \inv{P} A P \) 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
