Questions tagged [nullspace]

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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
1 answer

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
1 answer

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
1 answer

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 ...
1 vote
2 answers

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 ...
2 votes
0 answers

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
1 answer

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
0 answers

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
1 answer

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 ...