Definition:Congruence Transformation

Definition

Let $\mathbf A$ and $\mathbf B$ be matrices over $\R$.

A congruence transformation is a mapping from $\mathbf A$ and $\mathbf B$ of the form:

$\mathbf B = \mathbf P^\intercal \mathbf A \mathbf P$

where $\mathbf P^\intercal$ denotes the transpose of $\mathbf P$.

Also see

• Results about congruence transformations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): matrix (plural matrices): $(2)$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): congruence transformation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): matrix (plural matrices): $(2)$