Abstract: This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a ...

Abstract: This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a ...

We are now ready to define vector spaces. The idea is to observe that sets of column vectors, or row vectors, or more generally matrices of a given size, all come equipped with a notion of addition ...

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 ...

Algebra Module with Python For the Spanish version, click here Linear Algebra is a branch of mathematics that explores concepts such as vectors, matrices, tensors, systems of linear equations, and, in ...

Suppose that $V$ is finite-dimensional and $U$ and $W$ are subspaces of $V$. There is a basis $v_1, \dots, v_n, u_1, \dots, u_m, w_1, \dots, w_p$ of $U + W$ such that ...

ABSTRACT: Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map on its cyclic subspace. By ...

There are some familiar properties of vector addition and scalar multiplication — like the fact that if you multiply a vector by the scalar zero, you get the zero vector — which aren’t listed in the ...