# Questions tagged [linear-algebra]

Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.

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### Column-normalized inverse?

Suppose we define $A^{*}$ of positive definite $A=X'X$ using following two steps: let $B=A^{-1}$ scale columns of $B$ to obtain a matrix with $1$'s on the diagonal For the case of singular $A$, we ...
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### Choice between using Moore-Penrose inverse and G2 inverse

Moore-Penrose inverse for an arbitrary matrix $X\in \mathbb{R}^{n \times p}$ is defined by a matrix $X^\dagger$ satisfying all of the Moore-Penrose conditions, namely \begin{align} (1) \;\;\;& XX^\...
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### Numerical representation of linear spaces

A linear space in mathematics is a set whose elements (vectors) have operations of addition and multiplication by a scalar defined in such a way that certain properties are satisfied (commutativity, ...
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### Is there an algorithm or graph theory that allows me to not need to store an intermediate matrix when calculating AT*Y1*A + BT*Y2*B?

I have a system of conductors for which there are two dense matrices of the (complex) mutual admittances, $Y_A$ and $Y_B$, which are symmetric. Then, an equivalent nodal admittance matrix $Y_N$ is ...
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### Using submatrices of matrix decomposition for solving a large number least-squares problems

I want to decrease the computational time for solving a large number (>1000) of least-squares problems. Given a matrix, the system matrix for each least-squares problem is a submatrix of the given ...
1 vote
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1 vote
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### Efficiency of scipy.sparse.linalg.expm_multiply with sparse vs unsparse vectors

From the package scipy.sparse.linalg in Python, calling expm_multiply(X, v) allows you to compute the vector ...
1 vote
87 views

### Matlab - Equality between 2 Fisher matrices constructed in a different way

I want to know if, on a Fisher matrix, the projection operation (with a Jacobian matrix) commutes with a matricial inversion operation. The 2 ways to build these 2 matrices are: 1) First method: 1.1) ...
60 views

### PLASMA usage (Linear algebra routines that supports multithreading)

I have been looking for linear algebra libraries that support multithreading. I have found PLASMA which looks promising. It is from the same group that developed LAPACK. http://icl.cs.utk.edu/...