v1j4y
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Prove this trigonometric identity
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Using $2\cos(A)\cos(B)=\cos(A+B)+\cos(A-B)$, and $\cos^2(A)=\frac{\cos(2A)+1}{2}$ $\sin^2(A)=1-\cos^2(A)$ Solution with minimum steps: Using $(3)$ $$ 16\left(1-\cos^2(\theta)\right)\cos^3(\theta)=...

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Symmetrize eigenvectors of degenerate (repeated) eigenvalue
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The solution of Lagerbaer has been tested and i present the results obtained by sympy : (A) [0 1 1] [ ] [1 0 1] [ ] [1 1 0] (S) [0 1 0] [ ...

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understanding projection matrices
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I found this approach helpful so I would like to share it. Useful results, if $P$ is a projection matrix then: $ P\circ P = P$ , i.e projector $P$ projects the kernel onto itself. $ Pv=v\ \forall\ v\...

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