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Orthogonal matrix
Real square matrix whose columns and rows are orthogonal unit vectors
Orthogonal matrix
In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way to express this is Q T Q = Q Q T = I , {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: Q T = Q − 1 , {\displaystyle Q^{\mathrm {T} }=Q^{-1},} where Q−1 is the inverse of Q. An orthogonal...
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