Math 260, Spring 2017, Assignment 11

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

- Saint Augustine

Carefully define the following terms, then give one example and one non-example of each:

1. Othonormal set.

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

1. Formula for $\left\lbrack \vec{x}\right\rbrack_{\mathcal{B}}$ when $\mathcal{B}$ is an orthonormal basis.
2. Theorem relating orthonormality of a set to dot products of pairs of its elements.

Carefully describe the following algorithms:

1. Gram-Schmidt orthonormalization process.

Solve the following problems:

1. Section 5.2, problems 1, 3, 5, 13, 29, 33, and 35.

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