Category:Matrix Equivalence

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This category contains results about Matrix Equivalence.
Definitions specific to this category can be found in Definitions/Matrix Equivalence.

Let $R$ be a ring with unity.

Let $\mathbf A, \mathbf B$ be $m \times n$ matrices over $R$.

Definition 1

Let there exist:

an invertible square matrix $\mathbf P$ of order $n$ over $R$
an invertible square matrix $\mathbf Q$ of order $m$ over $R$

such that:

$\mathbf B = \mathbf Q^{-1} \mathbf A \mathbf P$

Then $\mathbf A$ and $\mathbf B$ are equivalent.

Definition 2

$\mathbf A$ and $\mathbf B$ are equivalent if and only if they are the relative matrices, to (possibly) different ordered bases, of the same linear transformation.

Pages in category "Matrix Equivalence"

This category contains only the following page.