Definition:Similarity Transformation

Definition

Let $\mathbf A$ and $\mathbf B$ be similar matrices.

A similarity transformation is an operation of changing $\mathbf B$ to $\mathbf A$ by multiplying $\mathbf B$ by a nonsingular matrix $\mathbf Y$ and its inverse $\mathbf Y^{-1}$ such that:

$\mathbf A = \mathbf Y^{-1} \mathbf B \mathbf Y$

Also known as

A similarity transformation is also known as:

a collinearity transformation

a collineation.

Also see

• Results about similarity transformations can be found here.

Sources

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