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The trace of an n × n square matrix A is defined as [1] [2] [3]: 34 = = = + + + where a ii denotes the entry on the i th row and i th column of A. The entries of A can be real numbers , complex numbers , or more generally elements of a field F .
In computer programming, tracing garbage collection is a form of automatic memory management that consists of determining which objects should be deallocated ("garbage collected") by tracing which objects are reachable by a chain of references from certain "root" objects, and considering the rest as "garbage" and collecting them.
a labeling V 2 → Hom(V,V) associating each degree-2 vertex to a linear transformation. Note that V 2 and V n should be considered as distinct sets in the case n = 2. A framed trace diagram is a trace diagram together with a partition of the degree-1 vertices V 1 into two disjoint ordered collections called the inputs and the outputs.
In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra.
Lotus 1-2-3 is a discontinued spreadsheet program from Lotus Software (later part of IBM).It was the first killer application of the IBM PC, was hugely popular in the 1980s, and significantly contributed to the success of IBM PC-compatibles in the business market.
If L/K is separable then each root appears only once [2] (however this does not mean the coefficient above is one; for example if α is the identity element 1 of K then the trace is [L:K ] times 1). More particularly, if L/K is a Galois extension and α is in L, then the trace of α is the sum of all the Galois conjugates of α, [1] i.e.,
6.2.1 No trace in L p. 6.2.2 Generalized normal trace. 7 Application. Toggle Application subsection. 7.1 Existence and uniqueness of weak solutions.
Given a function :, the associated trace function on is given by = (), where has eigenvalues and stands for a trace of the operator. Convexity and monotonicity of the trace function [ edit ]