Tagged Questions
4
votes
1answer
220 views
Holomorphic function of a matrix
A statement is made below. The questions are:
(a) Is the statement true?
(b) If it is, does it appear in the literature?
Here is the statement.
For any matrix $A$ in $M_n(\mathbb C)$, write ...
11
votes
2answers
271 views
Characteristic polynomials exhaust all monic polynomials?
Let $A$ be an $n\times n$ matrix, then $\mathrm{char}_A(x):=\det(xI-A)$ is a monic polynomial of degree $n$. It is called the characteristic polynomial of $A$. My question is the converse:
Let ...
4
votes
3answers
123 views
Is this action of $\mathbb F[[x]]$ on $\bigoplus_{i=0}^{\infty}\mathbb F$ natural?
The title of my question has a field $\mathbb F$ in it, but to make sure I'm not losing anything, I would like to introduce my question in full generality. But still, I will be happy with an answer in ...
2
votes
1answer
49 views
How can I solve a polynominal of degree 2 with more than one variable?
(Sorry if the title is not informative)
How can I find the value of matrices $F$ and $d$, in the following equation:
$$y'Ay+b'y+c'c = (y-d)'F(y-d)$$
Given $A:n \times n$, which is positive definite ...
