# Questions tagged [nullspace]

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### 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 ...
153 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: $$A \mathbf{x} = \mathbf{0}$$ ...
333 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-...
196 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 ...
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 ...
I need to solve the following equation: $$\begin{pmatrix} \frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\ \mu_z^{-1}k_xk_y &\... 1 vote 2 answers 192 views ### Finding null vectors of a parameter-dependent matrix I have dense complex matrices M(z) in which each element M_{ij} = M_{ij}(z) depends on a complex parameter z. I need to find z such that the matrix M gets singular, i.e. I am looking for ... 1 vote 1 answer 209 views ### Calculate the intersection of two matrix kernels in MATLAB If we have a discrete saddle point problem with the coefficient matrix$$ \mathcal{A} = \begin{bmatrix} A & B^T \\ B & 0 \end{bmatrix},  then $\mathcal{A}$ is invertible, supposing $... 0 votes 1 answer 114 views ### Method to calculate solution of a linear equation system? I am searching a solution method for the following equation system of equation systems: Let$A, B \in \mathbb{R}^{n \times n}$be s.p.d. Matrices and$O\$ be the zero matrix of the same size. Further ... 