Linear Algebra and the C Language/a0lg


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:

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