Tagged Questions
8
votes
5answers
170 views
Matrices with eigenvalues 0 and 1
How can you describe all $2\times 2$ matrices whose eigenvalues are 0 and 1?
My attempt:
I know that 0 and 1 has to be solutions of the characteristic polynomial. And I've considered some examples ...
1
vote
2answers
69 views
Eigenvalues and IVPs
So I have this question:
Solve the initial value problem:
$$\begin{align*}
\frac{dx_1}{dt}&=3x_3-2x_4,\\
\frac{dx_2}{dt}&=-2x_3+3x_4,\\
\frac{dx_3}{dt}&=3x_1-2x_2,\\
...
0
votes
1answer
243 views
Bessel Function in Sturm-Liouville problem
I have the following Sturm-Liouville problem:
$$\frac{d^2 y}{dx^2}+\lambda x^2y=0,$$
where $y(0)=0$ and $y(1)=0$.
I have solved this using MAPLE and found the exact solution to be:
...
1
vote
1answer
336 views
Mahalanobis Distance using Eigen-Values of the Covariance Matrix
Given the formula of Mahalanobis Distance:
$D^2_M = (\mathbf{x} - \mathbf{\mu})^T \mathbf{S}^{-1} (\mathbf{x} - \mathbf{\mu})$
If I simplify the above expression using Eigen-value decomposition ...
0
votes
1answer
33 views
Prove diagonalizability of a continuous transform
We've been going over diagonalization in my linear algebra class, but we've only been dealing with matrices—nothing too complicated. All of a sudden this problem came along and blindsided me:
Let V ...
0
votes
1answer
89 views
Eigenfunction of $(a(x) f^{II})^{II}= - \lambda^2f$
I need the eigenfunctions $f$ and eigenvalues $\lambda$ of $(a(x) f^{II}(x))^{II}= - \lambda^2f$ for a given $a(x)$.
For $a(x)$ constant the solution is a combination of sin, cos, sinh and cosh.
...
