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QR factorization

QR factorization is a decomposition of a matrix $A$ into a product $A = QR$ of an orthonormal matrix $Q$ and an upper triangular matrix $R$. Here, we conduct QR factorization using three different algorithms.

  • The algorithm based on Gran-Schmidt orthogonalization for square matrices with full rank (non-singular matrices)

  • The algorithm based on the column principal elements of the Householder matrix.

  • The algorithm based on Givens variation (only used for square arrays and has no column primitives).

These methods have their own advantages and disadvantages. Generally, we first choose householder method.