in this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl‎. ‎308 (2000) 203-211] and [linear algebra appl‎. ‎428 (2008) 2177-2191]‎.

The purpose of this note is to describe when a general complex algebraic $^*$-algebra pre-$C^*$-normed, and investigate their structure the $^*$-algebras are Baer $^*$-rings in addition algebraicity. As main result we prove following theorem for $^*$-algebras: every kind can be decomposed as direct sum $M\oplus B$, where $M$ finite dimensional $B$ commutative $^*$-algebra. summand $^*$-isomorph...

This work connects two mathematical fields – computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system, deciding solvability of a linear system, computing inverse matrix, eigenvalues, checking positive (semi)definiteness or stability. We discuss these problems and relati...

this paper presents as a brief introduction , the basic principles of matrix algebra for an alysing the power system problems with digital computers. the material contained in the text are as follows: primitive network, topology of electrical network, transformation of coordinates, bus admittance and bus impedance matrix.

We consider a noncommutative version of the bispectral problem proposed originally by Grünbaum. The latter had number unexpected connections with soliton theory and special functions interest in Mathematical Physics. take an algebraic route to describe symmetry structure algebras operators using notion full rank one algebra. By this concept, we provide general framework derive method verify if ...

Let M denote the multiplicative semigroup of all n-by-n matrices over a finite field F and K a commutative ring with an identity element in which the characteristic of F is a unit. It is proved here that the semigroup algebra K[M] is the direct sum of n + 1 algebras, namely, of one full matrix algebra over each of the group algebras K[GL(r, F)] with r = 0, 1, ..., n . The degree of the relevant...

Matrix algebra is one of the most useful tools in many disciplines, in particularly those related to data analysis (statistics, signal processing, machine learning, etc.). This short tutorial intends to provide a brief summary of the most important facts relating to matrix algebra for a person that has taken a linear algebra course a long time ago and has forgotten most of the details. Although...

In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.