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The 14 pages that link to Orthogonal matrix, each with the reason it gives.

• Rotation matrixNarrower topic: Every rotation matrix is orthogonal, but orthogonal matrices may also include reflections.

• OrthogonalityBroader topic: Such matrices encode transformations that preserve inner products and lengths.

• Identity matrixCompared with: Orthogonal matrices generalize the identity's inverse relation while allowing nontrivial transformations.

• EigenvectorCompared with: Its real eigenvectors, when present, have eigenvalues restricted to plus or minus one.

• QR decompositionBroader topic: The factor Q preserves lengths and angles, which helps make QR computations numerically stable.

• Symmetric matrixRelated: Its columns form the orthonormal eigenbasis used in diagonalization.

• Permutation matrixNarrower topic: Every permutation matrix is orthogonal because its rows and columns are orthonormal.

• Rigid motionRelated: Its linear action preserves distances and supplies the rotational or reflective part of a rigid motion.

• Diagonal matrixCompared with: Orthogonal matrices preserve lengths and angles, while diagonal matrices generally rescale coordinates.

• Matrix theoryBroader topic: Orthogonal matrices preserve geometry, unlike general matrices that distort it.

• Euler's rotation theoremRelated: Rotation matrices are orthogonal, a property that constrains their eigenvalues.

• Triangular matrixCompared with: Orthogonality constrains lengths and angles; triangularity constrains where entries can be nonzero.

• Hadamard conjectureRelated: Scaling a Hadamard matrix by the reciprocal square root of its order produces an orthogonal matrix.

• Cochran's theoremRelated: Orthogonal changes of coordinates diagonalize the standard normal decomposition behind the theorem.