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May
23
revised Solution Space - Linear Algebra
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May
23
answered Solution Space - Linear Algebra
May
20
answered What is the importance of phase spectrum in Fourier transform
May
20
answered Do planes stop, or are they ever expanding?
May
5
awarded  Teacher
May
5
revised Permutation Problem need help
added 1 character in body
May
5
answered Permutation Problem need help
May
5
asked Find a basis for the space of $2 \times 2$ matrices whose entries sum to $0$, and then find its orthogonal complement.
May
4
accepted If an $n\times n$ matrix $A$ is diagonalizable and has only one eigenvalue $\lambda$ with multiplicity $n$, then $A = \lambda I$. True or False?
May
4
comment If an $n\times n$ matrix $A$ is diagonalizable and has only one eigenvalue $\lambda$ with multiplicity $n$, then $A = \lambda I$. True or False?
Thanks, forgot to use that instead.
May
4
asked If an $n\times n$ matrix $A$ is diagonalizable and has only one eigenvalue $\lambda$ with multiplicity $n$, then $A = \lambda I$. True or False?
May
4
accepted Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
May
4
comment Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
@Ian Quick question, you said one of the eigenvectors has multiplicity 2. Do you mean in regard to the multiplicity MATLAB produces, or in regard to the actual eigenvectors - since $\lambda = 1$ has algebraic multiplicity 3, and geometric multiplicity 2?
May
4
comment Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
@Ian Of course, go head and post it as an answer.
May
4
comment Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
@Ian That's somewhat irritating that $eig$ runs into this problem. However, it's good to know its limitations - and to know that I was doing the problem right. As a side note, I tested it on Wolfram Alpha, and it finds the correct eigenvectors, but it also tries to find a third eigenvector. The third "eigenvector", though, is simply the zero vector so it can be ignored.
May
4
comment Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
@Ian Interesting. That's good to know. Also, why, then, does the Kernel differ from the first two eigenvectors produced by MATLAB? I multiplied $A$ by the vectors in my Kernel, and they are indeed eigenvectors. Furthermore, The first two eigenvectors of of the ones MATLAB found are linearly dependent, so it seems like it really only found one eigenvector.
May
4
revised Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
added 176 characters in body
May
4
asked Finding the eigenvectors of a matrix that has one eigenvalue of multiplicity three
May
3
accepted How to derive the discrete fourier transform of $(n+2)a^nu[n]$ where $|a| < 1$?
Mar
28
accepted How does equality in Bessel's Inequality prove an orthonormal complete sequence?