sum trace
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trace — trace1 [trās] n. [ME < OFr < tracier < VL * tractiare < L tractus, a drawing along, track < pp. of trahere, to DRAW] 1. Obs. a way followed or path taken 2. a mark, footprint, etc. left by the passage of a person, animal, or thing… … English World dictionary
Trace (linear algebra) — In linear algebra, the trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii represents the entry on the ith row and ith column … Wikipedia
Trace class — In mathematics, a trace class operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis. Trace class operators are essentially the same as nuclear operators, though many… … Wikipedia
trace — trace1 /trays/, n., v., traced, tracing. n. 1. a surviving mark, sign, or evidence of the former existence, influence, or action of some agent or event; vestige: traces of an advanced civilization among the ruins. 2. a barely discernible… … Universalium
trace — I [[t]treɪs[/t]] n. v. traced, trac•ing, 1) a surviving mark, sign, or evidence of the former existence, influence, or action of some agent or event; vestige 2) a barely discernible indication or evidence of some quantity, quality, characteristic … From formal English to slang
trace — trace1 verb 1》 find by investigation. ↘find or describe the origin or development of. 2》 follow the course or position of with one s eye, mind, or finger. 3》 copy (a drawing, map, or design) by drawing over its lines on a superimposed piece… … English new terms dictionary
Kloosterman sum — In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let a , b , m be natural numbers. Then :K(a,b;m)=sum {0leq xleq m 1, gcd(x,m)=1 } e^{2pi i (ax+bx^*)/m},Here x* is the inverse of x modulo m . They are named for the Dutch … Wikipedia
Partial trace — In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator valued function. The partial trace has applications in… … Wikipedia
Field trace — In mathematics, the field trace is a linear mapping defined for certain field extensions. If L / K is a finite Galois extension, it is defined for α in L as the sum of all the conjugates: g (α)of α, for g in the Galois group G of L over K . It is … Wikipedia
Selberg trace formula — In mathematics, the Selberg trace formula is a central result, or area of research, in non commutative harmonic analysis. It provides an expression for the trace, in a sense suitably generalising that of the trace of a matrix, for suitable… … Wikipedia
Dixmier trace — In mathematics, the Dixmier trace, introduced by Jacques Dixmier (1966), is a non normal trace on a space of linear operators on a Hilbert space larger than the space of trace class operators. Some of its applications to noncommutative… … Wikipedia
