It is an easy consequence of the Jordan canonical form that a matrix A ∈Mn×n(C) can be decomposed into a sum A = DA + NA where DA is a diagonalizable matrix, NA a nilpotent matrix, and such that DANA = NADA. It is clear that both DA and NA also commute with A. This decomposition is often referred to as the Jordan decomposition and has found many applications throughout the years. For example, i...

Abstract The paper is devoted to the generalization of Vinberg theory homogeneous convex cones. Such a cone described as set “positive definite matrices” in commutative algebra ? n Hermitian T-matrices. These algebras are Euclidean Jordan and consist × matrices A = ( ij ), where ii ? ?, entry for i < j belongs some vector space V ; ????) $$ {a}_{ji}={a}_{ij}^{\ast }=\mathfrak{g}\left({a}_{ij...

s of all papers presented at the meeting are given below. Papers read by title are indicated by the letter t" Paper number 48 was presented by Professor Chatland, number 54 by Mr. Block, number 58 by Professor Ulrich, number 72 by Mr. Kelly, and number 82 by Dr. Moise. ALGEBRA AND THEORY OF NUMBERS 47/. A. A. Albert: Power-associative rings. I I . A power-associative algebra A over a field F is...

We complete the analysis of the symmetry algebra L for systems of n second-order linear ODEs with constant real coefficients, by studying the case of coefficient matrices having a non-diagonal Jordan canonical form. We also classify the Levi factor (maximal semisimple subalgebra) of L, showing that it is completely determined by the Jordan form. A universal formula for the dimension of the symm...