In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction ...

Abstract: Riccati matrix equation (RME), a critical nonlinear matrix equation in autonomous driving and deep learning. However, memory-compute separation in traditional solving systems leads to ...

Abstract: A closed formula is given, which allows the determination of the impulsive solutions of linear homogeneous matrix differential equations (LHMDE) directly in terms of finite and infinite ...

In this work, we extend the theory of differential equations through a new way. To do this, we give an idea of differential–anti-differential equations and dene ordinary as well as partial ...

In "Finite Iterative Solutions to Periodic Sylvester Equations" by Lv and Zhang consider the periodic Sylvester matrix equations (PSMEs), which take two forms: $$A_jX ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Originally, I first had the idea for this app during a math class in my final high school year. I was fascinated by how equation systems could be solved using matrices and logical patterns, and so I ...

In this paper, collocation method based on Bernoulli and Galerkin method based on wavelet are proposed for solving nonhomogeneous heat and wave equations. The two methods have the linear systems ...