Calculate projections of vectors

ConeOfIce
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Homework Statement


Consider the following two vectors v1= (cosx , sinx)(transpose) , v2= (-sinx , cosx)(transpose). Compute the projectors P1, P2 onto the vectors v1 and v2.


Homework Equations


(a1) (a1*,b1*) (A) <---input
(b1) ...(B)
This is a matrix
that projects on
column
(a1)
(b1)

The snowman (one bracket over the other) is supposed to be a vector.

The Attempt at a Solution



I am completely lost on this situation. The textbook is extremely unclear, and there doesn't seem to be any information on line for how you go about projectors. Am I supposed to replace the input vector with v1, and then multiply it by the matrix to see what I get, or am I supposed to solve for a1 and b1, which I presume would be the projector. Any feedback would be great

Sorry if this comes out ugly.
Thanks.
 
Physics news on Phys.org
What are a1* and b1*? Is the projection you defined idempotent?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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