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Questions tagged [nullspace]

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5
votes
1answer
95 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 ...
1
vote
0answers
65 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
145 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 $...
4
votes
0answers
224 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
115 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
168 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 ...