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4
votes
1answer
79 views
Matrix Norm set #2
As a complement of the question
Matrix Norm set
and in order to complete the Problem 1.4-5 from the book: Numerical Linear Algebra and Optimisaton by Ciarlet. I have this additional conditions:
(3) ...
3
votes
4answers
64 views
The matrix has rank $n$ if and only if $A$ is nonsingular and $B = A^{-1}$.
Let $A$ and $B$ be $n \times n$ matrices with real entries. Show that the
matrix $$M = \left( \begin{matrix} A&I\\ I&B \end{matrix} \right)$$
has rank $n$ if and only if $A$ is nonsingular
...
1
vote
0answers
23 views
Is $\phi^T_tP_t^{-1}\phi_t\to 0$ when $P_{t+1}=\sum_{k=0}^t\phi_k\phi_k^T+P_0$?
Let $\phi_t\in\mathbb{R}^n$, $\forall t\geq0$, and $\sup_t\|\phi_t\|_2^2\leq M<\infty$(euclidean norm). Define $n\times n$ positive definitive matrices as follow,
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0
votes
2answers
33 views
Linear Algebra : find the kernel of this transformation.
Q. I think I find the kernel but several... which is correct? Seems like depending on which variable I put as kernel, I can get several kernels. Correct?
T is the transformation from $\mathbb{R}^2$ ...
