How to compute basis for the range, nullspace etc. of a matrix? 6 Approaches
The four fundamental spaces of a matrix $A$, namely the range and the nullspace of itself $A$ or its transpose $A^T$, are the heart of linear algebra. We often find ourselves in need of computing a basis for the range or the nullspace of a matrix, for theoretical or applicational purposes. There are many ways of computing a basis for the range or nullspace for $A$ or $A^T$. Some are better for application, either due to their robustness against floating point…
How can we compute basis for Nullspace?
There are at least two answers to this question; one of these is more educative and the other one is at least as educative (in a different and profound way) as well as practical. Method 1 The first method is a more introductory level method. It is helpful to know it and good to read it as a refresher even if one is more advanced student of the topic. A linear system $\mathbf{Ax=b}$ is homogeneous when $\mathbf b=\mathbf 0$ and nonhomogeneous…