Orthogonal Matrix

Topics: Algebra - Matrix - Orthonormal and Orthogonal Set

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(definition)

A $Q$ matrix of size $n\times n$ is called orthogonal if $Q^{-1}=Q^t$.

(observation)

If $Q^{-1}=Q^t⟹Q^{t}Q=I_n$

(theorem)

A $Q$ matrix of size $n\times n$ is orthogonal if and only if the columns of $Q$ build an orthonormal basis for ${\mathbb{R}}^n$.