scholarly journals Limit properties of monotone matrix functions

2012 ◽  
Vol 436 (5) ◽  
pp. 935-953
Author(s):  
Jussi Behrndt ◽  
Seppo Hassi ◽  
Henk De Snoo ◽  
Rudi Wietsma
Keyword(s):  
Matrix Functions ◽  
Monotone Matrix

scholarly journals Some convex and monotone matrix functions

1996 ◽  
Vol 248 ◽  
pp. 47-60
Author(s):  
Jaspal Singh Aujla ◽  
H.L. Vasudeva
Keyword(s):  
Matrix Functions ◽  
Monotone Matrix

Inequalities for some Monotone Matrix Functions

1969 ◽  
Vol 21 ◽  
pp. 485-494 ◽  
Author(s):  
Marvin Marcus ◽  
Paul J. Nikolai
Keyword(s):  
Vector Space ◽  
Applied Mathematics ◽  
Positive Definite ◽  
Inner Product ◽  
Complex Numbers ◽  
Matrix Functions ◽  
Unitary Space ◽  
Linear Map ◽  
Class Of Functions ◽  
Monotone Matrix

Let V denote a unitary vector space with inner product (x, y). A self-adjoint linear map T: V → V is positive (positive definite) if (Tx, x) ≧ 0 ((Tx, x) ≧ 0) for all x ≠ 0 in V. We write S ≧ T(S > T) if S and T are self-adjoint and S – T ≧ 0 (S – T > 0). If U is a unitary vector space, a function f: Hom(V, V) → Hom(U, U) is monotone idf S ≧ T implies that f(S) ≧ f(T). If both U and V are taken to be the n-dimensional unitary space Cn of n-tuples of complex numbers with standard inner product, then f is a monotone matrix junction, a notion introduced for a more restrictive class of functions by Löwner (3) which has important applications in pure and applied mathematics. For orientation we refer the reader to (1), where several interesting examples of monotone and related functions are displayed in detail.

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