Unlike PCA, this technique will not necessarily produce orthogonal vectors.
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Conversely, if, then is padded by orthogonal vectors from the kernel.
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Nonzero pairwise orthogonal vectors are always linearly independent.
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Many important results in linear algebra deal with collections of two or more orthogonal vectors.
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Let be the orthogonal vector field.
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Constructed the Suzuki groups as the subgroup of the symplectic group in 4 dimensions preserving a certain product on pairs of orthogonal vectors.
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Its rows are mutually orthogonal vectors with unit norm, so that the rows constitute an orthonormal basis of " V ".
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A similar approximation technique by trigonometric functions is commonly called Fourier expansion, and is much applied in engineering, see basis of orthogonal vectors.
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Lattice reduction algorithms aim, given a basis for a lattice, to output a new basis consisting of relatively short, nearly orthogonal vectors.
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A further generalization of the Pythagorean theorem in an inner product space to non-orthogonal vectors is the " parallelogram law ":
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