# Fields for Which the Principal Axis Theorem Is Valid

by A. Charnow (California State University -- Hayward) and E. Charnow (California State University -- Hayward)

This article originally appeared in:
Mathematics Magazine
October, 1986

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

One version of the Principal Axis Theorem asserts that any symmetric matrix with entries in $$\mathcal{R}$$ is similar over $$\mathcal{R}$$ to a diagonal matrix.  The authors find necessary and sufficient conditions for a field $$K$$ that make the Principal Axis Theorem valid over $$K$$.

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Capsule Course Topic(s):
Linear Algebra | Symmetric Matrices