Math 260, Fall 2017, Assignment 10

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

Read:

1. Section 5.2.

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

1. Orthogonal transformation (a.k.a. length-preserving transformation).

Carefully describe the following algorithms:

1. Gram-Schmidt orthonormalization process.

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

1. Theorem concerning $QR$ decomposition.
2. Pythagorean theorem.

Solve the following problems:

1. Section 5.2, problems 1, 3, 5, 7, 9, 15, 17, 19, 21, 23, 32, 33, and 35.

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