# Questions tagged [linear-algebra]

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### How to reduce an LP problem already in its standard form?

Suppose we have a feasible LP problem in its standard form. From Ax=b we can directly determine some of its variables and thus we can reduce the problem. For example, from two constraints: x+y+z=2 and ...
1 vote
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### explain Givens rotation chain for maintaining Cholesky factorization

I'm attempting to implement the dual face algorithm from Pan's book chapter 22 (https://link.springer.com/book/10.1007/978-981-19-0147-8). The part in question is pasted here: Can you please explain ...
1 vote
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### Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$

Let $\mathbf{A} \in \mathbb{R}^{n \times n}$. I'm working in a problem where I have a black-box algorithmic solution to compute the products $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T \mathbf{x}$ given ...
1 vote
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### Computing simplex tableu for a given basis

I found the following problem in my book. I know that I can compute the simplex tableau , let's call it S for a basis X_b=(x_1, x2, x_5)^T as ...
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### Finding all left inverses of a matrix

For large rectangular matrices, is this something that is easy or possible to achieve in the programming language R? Or to get all possible equations, must one solve equations by hand? I see notes ...
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### PhD-level textbooks on linear programming

My graduate Linear Programming class uses Bertsimas & Tsitsiklis's Introduction to Linear Optimization. Are there any alternative texts that I could use to supplement this textbook (mainly the ...
I have a polyhedral set for constraining $x$: \begin{align} \mathcal{P} = \{x \in \mathbb{R}^n_{+} : \ Dx \leq d \} \end{align} where $D \in \mathbb{R}^{m \times n}, d \in \mathbb{R}^m$. I find the ...