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2. Trace (linear algebra) - Wikipedia

   en.wikipedia.org/wiki/Trace_(linear_algebra)

   The trace of a Hermitian matrix is real, because the elements on the diagonal are real. The trace of a permutation matrix is the number of fixed points of the corresponding permutation, because the diagonal term a ii is 1 if the i th point is fixed and 0 otherwise. The trace of a projection matrix is the dimension of the target space.

3. Trace table - Wikipedia

   en.wikipedia.org/wiki/Trace_table

   A trace table is a technique used to test algorithms in order to make sure that no logical errors occur while the calculations are being processed. The table usually takes the form of a multi-column, multi-row table; With each column showing a variable , and each row showing each number input into the algorithm and the subsequent values of the ...

4. Field trace - Wikipedia

   en.wikipedia.org/wiki/Field_trace

   The trace form is used in algebraic number theory in the theory of the different ideal. The trace form for a finite degree field extension L/K has non-negative signature for any field ordering of K. [8] The converse, that every Witt equivalence class with non-negative signature contains a trace form, is true for algebraic number fields K. [8]

5. Trace class - Wikipedia

   en.wikipedia.org/wiki/Trace_class

   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.

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8. Lefschetz fixed-point theorem - Wikipedia

   en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem

   This formula involves the trace of the Frobenius on the étale cohomology, with compact supports, of ¯ with values in the field of -adic numbers, where is a prime coprime to . If X {\displaystyle X} is smooth and equidimensional , this formula can be rewritten in terms of the arithmetic Frobenius Φ q {\displaystyle \Phi _{q}} , which acts as ...

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