Some properties

Linear Algebra and the C Language · Wikibooks

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    Orthonormal basis:

    An orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors....

    Wikipedia: Orthogonal matrix

    Some properties

    Orthonormal basis:

    Compute x in the B basis :

    Proj(x) = A inv(AT A) AT = A inv(ID) AT = A AT:

    Orthonormal matrices preserve lengths:

    Orthonormal matrices preserve angles:

    Orthonormal matrices preserve the dot product: