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Chapter 8: Q39E (page 401)

For which angles 胃can you find a basis of鈩�nsuch that the angle between any two vectors in this basis is 胃?

Short Answer

Expert verified

The solution is

0<胃<cos1-1n-1

Step by step solution

01

to find two vectors in this basis is θ

Assuming that the angle between any two vectors is the same in an n-dimensional space, the angle is given by:

胃=cos1-1n-1

The angle between the vectors胃 should be between 0 and the above value in order to find a basis. As a result, we have:

0<胃<cos1-1n-1

Thus, we may discover a basis of 鈩�nsuch that the angle between any two vectors in this basis is for these values of angle 胃.

02

conclusion:

0<胃<cos1-1n-1

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