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"
The following 3 pages are in this category, out of 3 total.