We prove that the Ricci flow equation for left invariant metrics on Lie groups reduces to a first order ordinary differential equation for a map Q : (−a, a) → UT , where UT is the group of upper triangular matrices. We decompose the matrix Rij of Ricci tensor coordinates with respect to an orthonormal frame field Ei into a sum 1 Rij + 2 Rij + 3 Rij + 4 Rij such that, for any Ei′ = U i i′Ei with...

In this note, we introduce the concept of semi-*-IFP, involutive version semi-IFP, which is a generalization quasi-*-IFP and *-reducedness *-rings. We study basic structure properties *-rings having semi-*-IFP give results for IFPs in rings with involution. Several counterexamples are stated to connect versions IFP. discuss conditions be extended into *-subrings ring upper triangular matrices. ...

A triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. [6] For a square matrix M , M−1 is the inverse matrix where M ×M−1 = I and I denotes the n× n identity matrix. We say that the problem siz...

The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show s...