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Introduction to Linear Algebra

Exercise 1.2.33

Find 4 perpendicular unit vectors of the form $(\pm \frac{1}{2}, \pm \frac{1}{2}, \pm \frac{1}{2}, \pm \frac{1}{2}) :$ Choose $+$ or $−$ .

Answers

The columns of the 4 by 4 "Hadamard matrix" (times $\frac{1}{2}$ ) are perpendicular unit vectors:

\frac{1}{2} H = \frac{1}{2} [\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & - 1 & 1 & - 1 \\ 1 & 1 & - 1 & - 1 \\ 1 & - 1 & - 1 & 1 \end{matrix}]

mathchakra

2021-11-20 14:11

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