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squenshl
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Homework Statement
Let x = (x1,x2) [itex]\in[/itex] Rn, x1 [itex]\in[/itex] Rn1, x2 [itex]\in[/itex] Rn2, n1 + n2 = n and A [itex]\in[/itex] Rnxn be symmetric and positive definite.
a) Let x0 [itex]\in[/itex] Rn. Show that we can write (x-x0)TA(x-x0) = ||L(x-x0||22. Is L unique?
b) Consider the quadratic term b = xTAx. Show that we can write b = x1TBx1 + 2x1TCx2 + x2T
Dx2, and what are the matrices B, C, D?
Homework Equations
The Attempt at a Solution
a) Is it using the definition of symmetric & positive defintie matrices.
b) Isn;t that just a quadratic form?