DLA Terminology and notation

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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 $B = P^{- 1} A P$
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transition matrix: an invertible matrix $P$ that realizes a similarity relationship $B = P^{- 1} A P$ for similar matrices $A$ and $B$
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diagonalizable: a square matrix that is similar to a diagonal matrix
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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
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geometric multiplicity: the dimension of the corresponding eigenspace
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