Abstract:

The paper  exhibits the general matrix function   dx(A)=∑[DD(X]σ∈H[DD)]χ(σ)∏[DD(]m[]i=1[DD)]aiσ(i) as an inner product in a suitable symmetric class of tensors on a unitary space. It is then used the Schwarz inequality and operator norm to obtain three main inequalities in the variation for general matrix functions, one of which the inequalities  extend is wellknow the inequalitity.

Key words: General matrix functions, Tensor product;Symmetry operator, Schwarz inequality, Operator , norm