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Exercise 1.8.15

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Every 3 by 3 matrix has 9 entries. So $U Σ V^{T}$ must have 9 parameters. There are 3 parameters in $Σ$ . Each of $U$ and $V$ shall have 3 parameters.

For 4 by 4 matrix, there are 4 parameters for $Σ$ , since $U$ , $V$ have the same shape, they have $(16 - 4) \div 2 = 6$ parameters each.

There are 3 parameters to describe a rotation in a 4-dimensional space. (TODO)

niuers

2020-03-20 00:00

Exercise 1.8.15

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