Definition:Orthogonal Transformation

Definition

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

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

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

Also see

• Results about orthogonal transformations can be found here.

Sources

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