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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
0
answers
619
views
Understanding canonical angles between two subspaces
I am trying to understand Wedin Theorem on the perturbations of the Singular Vectors of a matrix, and a key element for this theorem is the matrix of the canonical angles between two subspaces; I am m …
0
votes
1
answer
1k
views
SVD alternatives for symmetric matrices
Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices
$$
A = E'E
$$
Practically this can be done easily using SVD decompos …
0
votes
1
answer
719
views
Unique solution to a matrix equations [closed]
Given any $n \times k$ real matrix $M$, where $n<k$ and $rank(M)=n$, I consider the following equation (where $M'$ is the transpose of $M$):
$$
MM' = MAM'
$$
Then clearly, $A = \mathbb{1}_k $, the $ …
5
votes
1
answer
763
views
Perturbations on the pseudoinverse of a matrix
Given a matrix $A \in \mathbb{R}^{n\times m}$, and its perturbation
$$
A_p = A + \Delta
$$
is there a way to represent
$$
(A_p)^{\star}= (A)^{\star} + f(\Delta)
$$
where $(A_p)^{\star}$ ($(A)^{\star …
2
votes
0
answers
130
views
SVD when only off-diagonal terms are known
I have a real matrix $A \in \mathbb{R}^{n\times n}$ such that:
$A$ is symmetric
All the off-diagonal terms are known and positive
Has rank $k<n$
Unfortunately I don't know the values of the diagon …