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  • 0 posts edited
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21h
revised Conjugating rotation by another rotation
deleted 715 characters in body
22h
revised Conjugating rotation by another rotation
added 606 characters in body
23h
revised Conjugating rotation by another rotation
added 606 characters in body
1d
comment Common Intersection Point of ellipsoids
@fuzzyrock1 I know what you mean but you must describe the condition mathematically.
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
Think about what $[T]_{\cal B}$ means.
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
You're right; $T$ would need to be normal. But orthogonality isn't needed to prove the result.
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
Because of orthogonality.
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
Won't $B_2$ be $T$-invariant?
Feb
8
comment Area inside polar curve
There are two solutions.
Feb
8
comment Area inside polar curve
You need to solve $7\sin \theta =1$. However, these will not be nice angles and so you have to express them in terms of $\sin ^{-1}$.
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
If you extend to an orthonormal basis for $V$ then you get block diagonal form, not block upper triangular form
Feb
8
comment Existence of a block upper triangular form matrix representation for a linear operator
Start with a basis for $W$ and extend it to a basis for $V$. Then use the fact that $W$ is $T$-invariant.
Feb
8
comment Area inside polar curve
Arc length has nothing to do with area. Start by finding the intersection points of both curves.
Feb
8
comment Definition of Inverse in Linear and Abstract Algebra
For the second problem concerning the homomorphism, you already know that the inverse exits because you are in a group. Proving $\phi (a^{-1})=[\phi(a)]^{-1}$ is not equivalent to proving an inverse exists.
Feb
8
comment Spectral norm of lower triangular perturbation
You have that $L=A-I$ and so $\lVert L \rVert \le \lVert A \rVert +1< 2+\epsilon$.
Feb
8
comment Common Intersection Point of ellipsoids
@fuzzyrock1 You need to define the condition "unless one is contained in the other".
Feb
8
comment Common Intersection Point of ellipsoids
You need to formulate your condition in terms of major and minor axes.
Feb
8
comment Polar Equations (Complex)
If it's correct, you will need to use a calculator.
Feb
8
comment Imaginary tangents of parabola
It makes no sense to say that there are 2 imaginary tangents. What they really mean is that they got imaginary slopes for the lines.
Feb
8
comment Polar Equations (Complex)
Are you should you've copied the question correctly? The equation looks a little tough.