The bookUnit 1 · Eigenvalues and Canonical Forms26 / 83

Rational canonical form

Why this is asked: Rational canonical form works over any field — use it when the characteristic polynomial does not split. Invariant factors divide one another; the last one is the minimal polynomial.

Rational canonical form and invariant factors

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Rational canonical form, and when to prefer itinteractive

The form that exists over every field — and the divisibility chain that makes it unique.

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Let A, B be n×n matrices over $\mathbb{Q}$ . Which of the following are true?

Next: Gram–Schmidt, orthogonal/unitary/normal matrices, spectral theorem

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