Linear algebra forms the mathematical backbone of data science and machine learning algorithms. This comprehensive tutorial covers essential linear algebra concepts, from basic matrix operations to ...

This course focuses on lines and planes, the geometry and algebra of vectors, systems of linear equations, matrix algebra, linear independence, spanning sets, basis, linear transformations, ...

Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and ...

The paper compares of the multidimensional matrix algebra and the tensor algebra. It is shown that tensor algebra operations are realized in the multidimensional matrix algebra more efficiently.

In this study, we propose matrix-mimetic, tensor-algebraic formulations to preserve and process data in its native, multidimensional format. For a general family of tensor algebras we prove the ...