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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 psychology, multiple trace theory is a memory consolidation model advanced as an alternative model to strength theory. It posits that each time some information is presented to a person, it is neurally encoded in a unique memory trace composed of a combination of its attributes. [ 1 ]
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.
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 ]
Tracing is the most common type of garbage collection – so much so that "garbage collection" often refers to the tracing method, rather than others such as reference counting – and there are a large number of algorithms used in implementation.
A mixed state is described by a density matrix ρ, that is a non-negative trace-class operator of trace 1 on the tensor product . The partial trace of ρ with respect to the system B , denoted by ρ A {\displaystyle \rho ^{A}} , is called the reduced state of ρ on system A .