The groups of this type are ones that given a vector space over a field, preserve a non-degenerate quadratic form over that space.
The groups of this type are ones that given a vector space over a field, preserve a non-degenerate quadratic form over that space. Euler's conjecture on Graeco-Roman Squares was refuted for n=6 by finding this sort of matrix. Householder matricies are always symmetric and this. Linear transformations of this type preserve inner products. Fourier's theorem is dependent on trignometric functions having this property, which means the integral from negative pi to pi of sin kx times sin jx dx is only non-zero for k equals j. If the vectors in a basis are of unit length and this, then they are orthonormal. If the dot product of two vectors is zero, the vectors are this to each other. For 10 points, name this adjective used to describe lines or curves that are perpendicular.
The groups of this type are ones that given a vector space over a field, preserve a non-degenerate quadratic form over that space.
orthogonal