Questions tagged [nullspace]
The nullspace tag has no usage guidance.
9
questions
3
votes
0answers
113 views
Compute Nullspace of Sparse Matrix
I am computing the nullspace of a sparse rectangular $m$ x $n$ matrix $A$, where $m$ << $n$. I do this by computing the QR decomposition of $A^T$ and extract the $n-m$ right-most columns of the ...
5
votes
1answer
98 views
Accurately Computing a Positive Vector in the Nullspace of a Matrix
I'm sure this question has been asked before yet after many hours of searching I am unable to find a definitive answer.
The problem at hand is solving the linear system: $$A \mathbf{x} = \mathbf{0}$$ ...
0
votes
1answer
61 views
Method to calculate solution of a linear equation system?
I am searching a solution method for the following equation system of equation systems:
Let $A, B \in \mathbb{R}^{n \times n}$ be s.p.d. Matrices and $O$ be the zero matrix of the same size. Further ...
5
votes
1answer
156 views
Nullspace calculation of large matrix with rational numbers without round-off errors (exact)
I need to calculate a basis of the nullspace of large (up to a thousand columns and rows) matrices. For my application, it is very important that no round-off errors occur during the computation, so I ...
2
votes
0answers
358 views
finding null space to a complex matrix
I need to solve the following equation:
$$
\begin{pmatrix}
\frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\
\mu_z^{-1}k_xk_y &\...
1
vote
1answer
191 views
Calculate the intersection of two matrix kernels in MATLAB
If we have a discrete saddle point problem with the coefficient matrix
$$ \mathcal{A} =
\begin{bmatrix}
A & B^T \\
B & 0
\end{bmatrix},
$$
then $\mathcal{A}$ is invertible, supposing $...
5
votes
0answers
283 views
Is it possible to predict the null space of a structure from contributing elements null spaces?
I am trying to solve an almost incompressible problem with heterogeneous properties by domain decomposition. Solution with CG converges slowly or divergerces completely. My problem becomes ill-...
3
votes
1answer
147 views
Find a single vector in the null space
I have a single sparse matrix $A$ for which I can easily compute $Ax$ and $A^*x$ and I would like to solve $\min(||Ax||) \text{ s.t. } ||x||=1$. I know the answer is the right singular vector ...
1
vote
2answers
187 views
Finding null vectors of a parameter-dependent matrix
I have dense complex matrices $M(z)$ in which each element $M_{ij} = M_{ij}(z)$
depends on a complex parameter $z$. I need to find $z$ such that the matrix $M$
gets singular, i.e. I am looking for ...
