Math 218: Matrices and Vector Spaces

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The Gram-Schmidt Algorithm

We can calculate the projection of a vector v in the direction of v1 with the syntax (v1*v)/(v1*v1) * v1.

We can calculate the component of a vector v in the direction of v1 with the syntax (v1*v)/v1.norm().

The Gram-Schmidt algorithm is built into sage!

We can then use the Gram-Schmidt algorithm to calculate A=QR.