why are orthogonal matrices important?

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- September 16th 2011, 10:45 AMEuclidOrthogonal Matrices
why are orthogonal matrices important?

- September 16th 2011, 11:42 AMHallsofIvyRe: Orthogonal Matrices
Because they are

**easy**! More generally, we can think of any matrix as the "change of basis" matrix showing how the components of a vector change if you change from one basis to another. In particular, an orthogonal matrix is a "change of basis" matrix where both bases are "orthonormal" (all basis vectors have length 1 and are orthogonal to one another) and those are particularly simple bases. - September 16th 2011, 05:28 PMAckbeetRe: Orthogonal Matrices
From an applications standpoint, orthogonal matrices are important because rotations of a vector can be represented by an orthogonal matrix.