A canonical form under ϕ-equivalence

A Rational Canonical Form Algorithm

Canonical Equivalence Relations on Nets

We give a list of canonical equivalence relations on discrete nets of the positive unit sphere of c0. This generalizes results of W. T. Gowers [1] and A. D. Taylor [5].

On Equivalence and Canonical Forms

Decidability of de nitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of de nitional equality are based on a con uent, strongly-normalizing notion of reduction. Coquand has considered a di erent approach, directly proving the correctness of a practical equivalance algorithm based on the shape o...

Jordan Canonical Form

is the geometric multiplicity of λk which is also the number of Jordan blocks corresponding to λk . • The orders of the Jordan Blocks of λk must sum to the algebraic multiplicity of λk . • The number of Jordan blocks corresponding to an eigenvalue λk is its geometric multiplicity. • The matrix A is diagonalizable if and only if, for any eigenvalue λ of A , its geometric and algebraic multiplici...

The Jordan Canonical Form

Let β1, . . . , βn be linearly independent vectors in a vector space. For all j with 0 ≤ j ≤ n and all vectors α1, . . . , αk, if β1, . . . , βn are in the span of β1, . . . , βj, α1, . . . , αk, then j + k ≥ n. The proof of the claim is by induction on k. For k = 0, the claim is obvious since β1, . . . , βn are linearly independent. Suppose the claim is true for k−1, and suppose that β1, . . ....