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Linear Algebra (1.25-26.PKN25/M)
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Every vector in has a positive norm
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In the -factorization of a matrix , is an orthogonal matrix
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If is an inconsistent linear system, then is also inconsistent
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The Gram-Schmidt algorithm can be applied to every set of vectors in
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If columns of a matrix form an orthonormal set, then is orthonormal
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If a matrix preserves the norm of vectors (I.e., if for all ), then is orthogonal
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In the -factorization of a matrix , is an upper-triangular matrix
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If in is orthogonal to every vector of , then
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If a matrix preserves the angles between the vectors, then is orthogonal
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In the -factorization of a matrix , is an orthogonal matrix
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