227A-HW3

16 flashcards · Mathematics · by John Viljoen

1. take a standardised data matrix X:

3. given:

4. what is the cauchy swartz inequality for matrices?

6. what are the three properties of a norm?

   its value is larger than or equal to zero, with zero only being achieved for a trivial 0 input triangle inequality: norm(a+b) <= norm(a) + norm(b) homogenous with respect to scalar multiplication, norm(a*b) = a*norm(b) when a is a scalar

12. using 2 approaches:

14. given: where Sigma is the SVD Sigma, and w = V.T x, z = U.T y

15. Given that: and:

16. what is the rayleigh coefficient of a matrix and what are its properties?