Math 260, Fall 2019, Assignment 11

I have found a very great number of exceedingly beautiful theorems."

- Pierre de Fermat

Read:

1. Section 3.4, through Theorem 3.4.2.
2. Section 5.2.

Carefully state the following theorems (you do not need to prove them):

1. Formula for the coordinate vector $[\vec{v}]_{\mathcal{B}}$, when $\mathcal{B}$ is an orthonormal basis.
2. Theorem concerning $QR$-factorization.

Carefully describe the following algorithms:

1. Gram-Schmidt orthonormalization procedure.

Solve the following problems:

1. Section 5.2, problems 1, 3, 11, 13, 15, 17, 25, 27, 29, 33, and 35.

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