All Questions
7 questions
2
votes
1
answer
108
views
Is there an efficient way to compute the inverse of several symmetric matrices that share the same structure?
I have many symmetric matrices to be inverted. They all share the form
$A^\top D_{x_1} A$, $A^\top D_{x_2} A$, ... with $A\in\mathbb{R}^{n\times p}$, $n>p$ and $D_x$ positive diagonal but with ...
- 23
7
votes
3
answers
446
views
Does a symmetric positive definite matrix also have $\mathbf{A} = \mathbf{L}^T\mathbf{L}$ (where $\mathbf{L}$ is a lower triangular matrix)?
As we know, for a symmetric positive definite (SPD) matrix $\mathbf{A}$, there is a theorem about the Cholesky factorization $\mathbf{A}= \mathbf{L}\mathbf{L}^T$, where $\mathbf{L}$ is a lower ...
- 981
1
vote
1
answer
154
views
Mapping from n x n complex symmetric tridiagonal to 2n x 2n real symmetric tridiagonal
In my program I have a complex symmetric tridiagonal matrix. In order to perform some algorithmic optimizations I am searching for a (ideally linear) mapping from $n\times n$ complex symmetric ...
- 11
2
votes
1
answer
173
views
Is my matrix symmetric?
I obtained a mass matrix through Finite Elements discretization. Now, I want to check if it is symmetric. To do that I subtract to my matrix $M$ its transposed $M^T$. The result is another matrix of ...
- 173
3
votes
2
answers
1k
views
Get symmetric Finite Difference matrix in non Laplacian settings
I would like to solve a system of differential equations $u+\nabla(\nabla\cdot u)=f$ or in more detail
$a+\partial_t^2a+\partial_t\partial_xb+\partial_t\partial_yc=f$
$b+\partial_x^2b+\partial_x\...
- 143
5
votes
1
answer
566
views
What is the most efficient way to obtain the max eigenvalue of a specific symmetric matrix via Eigen C++
Suppose I have a symmetric matrix $A_{1000\times 1000}$, which can be represented by:
$A = J G J^T$
where $J$ in 1000x3 is full column rank dense matrix; $G$ in 3x3 is a nonsingular dense matrix.
...
- 759
1
vote
1
answer
357
views
Is there congruent transform implementation for dense symmetric matrix in Eigen(C++)?
I need to determine whether a real dense symmetric matrix is positive definite or not.
One possible way is to obtain all the eigen values and check the sign of the minimum eigen value but requires ...
- 759