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An Application of Sylvester's Rank Inequality

by Sidney H. Kung

This article originally appeared in:
College Mathematics Journal
March, 2011

Subject classification(s): Algebra and Number Theory | Linear Algebra | Eigenvalues and Eigenvectors
Applicable Course(s): 3.8 Linear/Matrix Algebra

Using two well known criteria for the diagonalizability of a square matrix plus an extended form of Sylvester's Rank Inequality, the author presents a new condition for the diagonalization of a real matrix from which one can obtain the eigenvectors by simply multiplying some associated matrices without solving a linear system of simultaneous equations.

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Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors
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