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If a 2 x 2 real matrix has zero trace, its square is a diagonal matrix. The trace of a 2 × 2 complex matrix is used to classify Möbius transformations. First, the matrix is normalized to make its determinant equal to one. Then, if the square of the trace is 4, the corresponding transformation is parabolic.
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal.
Then F b ≠ F c if b ≠ c. Moreover, the K-linear transformations from L to K are exactly the maps of the form F b as b varies over the field L. When K is the prime subfield of L, the trace is called the absolute trace and otherwise it is a relative trace. [4]
A trace diagram representing the adjugate of a matrix. In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly modified) graphs in which some edges are labeled by matrices. The simplest trace diagrams represent the trace and determinant of a matrix.
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.
Casio BASIC is a programming language used in the Casio calculators such as the ClassPad, PRIZM Series, fx-9860G Series, fx-5800P, Algebra FX and CFX graphing calculators.It is also known as "BasicLike" in some models.
Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics , including consistent histories and ...
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 ]