DLA Terminology and notation

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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 $B=\inv{P}AP$

transition matrix: an invertible matrix $P$ that realizes a similarity relationship $B=\inv{P}AP$ for similar matrices $A$ and $B$

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Note 25.2.1.

We have already used the term transition matrix to mean a change-of-basis matrix (see Section 22.2), and we will justify this double definition of the term when we study similarity in more generality in Chapter 26.

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
geometric multiplicity: the dimension of the corresponding eigenspace