The QR decomposition of a nonsingular matrix exists.

Created almost 9 years ago, updated about 8 hours ago

Every nonsingular real square matrix has a QR decomposition with orthogonal $Q$ and invertible upper triangular $R$. Gram–Schmidt proves existence by orthonormalizing its independent columns; Householder reflections are usually more stable computationally. Requiring positive diagonal entries of $R$ makes this real factorization unique.

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