Category:Matrix Congruence
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This category contains results about Matrix Congruence.
Definitions specific to this category can be found in Definitions/Matrix Congruence.
Let $R$ be a commutative ring with unity.
Let $n$ be a positive integer.
Let $\mathbf A$ and $\mathbf B$ be square matrices of order $n$ over $R$.
Then:
- $\mathbf A$ and $\mathbf B$ are congruent
- there exists an invertible matrix $\mathbf P \in R^{n \times n}$ such that $\mathbf B = \mathbf P^\intercal \mathbf A \mathbf P$
where $\mathbf P^\intercal$ denotes the transpose of $\mathbf P$.
Subcategories
This category has only the following subcategory.
C
- Congruence Transformations (empty)