Finding the QR decomposition of A, it exists because the columns of A are linearly independent.with( LinearAlgebra ): with( VectorCalculus ):

Warning, the names `&x`, CrossProduct and DotProduct have been rebound

Warning, the assigned names `<,>` and `<|>` now have a global binding

Warning, these protected names have been redefined and unprotected: `*`, `+`, `.`, D, Vector, diff, int, limit, series

A := Matrix( [[1,1,0,1],[-1,0,1,1],[1,1,1,1]]);

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Q is constructed from the orthnormalized columns of A using Gram Schmidt.orthonormCols := GramSchmidt( [Column( A, 1..4 )], normalized ): Q := Matrix( orthonormCols );

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R = Q^T * AR := Transpose( Q ) . A;

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Since A = Q * R, we should be able to regenerate the original matrix.Q . R;

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Just for demonstration purposes, here's how to accomplish the decomposition using a native maple call.(mQ,mR) := QRDecomposition(A, fullspan); mQ . mR;

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