# Category:Matrix Similarity

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This category contains results about **Matrix Similarity**.

Definitions specific to this category can be found in Definitions/Matrix Similarity.

Let $R$ be a ring with unity.

Let $n \in \N_{>0}$ be a natural number.

Let $\mathbf A, \mathbf B$ be square matrices of order $n$ over $R$.

### Definition 1

Let there exist an invertible square matrix $\mathbf P$ of order $n$ over $R$ such that $\mathbf B = \mathbf P^{-1} \mathbf A \mathbf P$.

Then $\mathbf A$ and $\mathbf B$ are **similar**.

### Definition 2

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

## Pages in category "Matrix Similarity"

This category contains only the following page.