Linear algebra is one of the most powerful branches of mathematics – and one of the most useful. It is at the heart of modern science, technology, and engineering. It is the foundation for everything ...

$$ \begin{align} \mathbb{R}^n &= \text{all (column) vectors with n real components} \\ &={,\underline{v}=(v_1,v_2,\cdots,v_n);\text{for each};v_i \in R,} \end{align ...

Welcome to MIT 18.06: Linear Algebra! The Spring 2025 course information, materials, and links are recorded below. Course materials for previous semesters are archived in the other branches of this ...

This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

ABSTRACT: In this paper, we have introduced a new generalized form of topological vector spaces, namely, almost β-topological vector spaces by using the concept of β-open sets. We have also presented ...

ABSTRACT: In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute ...

https://doi.org/10.4169/amer.math.monthly.119.01.065 https://www.jstor.org/stable/10.4169/amer.math.monthly.119.01.065 Abstract We compute the minimal cardinalities ...