# trace

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Related to trace: Traceroute, Trace route

## trace

^{1}

**1.**any line drawn by a recording instrument or a record consisting of a number of such lines

**2.**the postulated alteration in the cells of the nervous system that occurs as the result of any experience or learning

**3.**

*Geometry*the intersection of a surface with a coordinate plane

**4.**

*Maths*the sum of the diagonal entries of a square matrix

**5.**

*Meteorol*an amount of precipitation that is too small to be measured

## trace

^{2}

**1.**either of the two side straps that connect a horse's harness to the swingletree

**2.**

*Angling*a length of nylon or, formerly, gut attaching a hook or fly to a line

## Trace

The trace of a matrix is the sum of the matrix’s diagonal elements. This concept is defined only for a square matrix A . The trace of *A* is denoted by Tr *A* or Sp *A*. The latter symbol is derived from the German word *Spur*, which is sometimes used to refer to a trace. It follows that

Tr *A* = a_{11} + a_{22} + … + a_{nn}

If the characteristic equation of *A* has the roots (called eigenvalues or characteristic roots) λ_{1}, λ_{2},…,λ_{n}, then

*Tr A =* λ_{1} + λ_{2} + …. + λ_{n}

## trace

[trās] (computer science)

To provide a record of every step, or selected steps, executed by a computer program, and by extension, the record produced by this operation.

(electronics)

The visible path of a moving spot on the screen of a cathode-ray tube. Also known as line.

(engineering)

The record made by a recording device, such as a seismometer or electrocardiograph.

(geology)

The intersection of two geological surfaces.

(mathematics)

The trace of a matrix is the sum of the entries along its principal diagonal. Designated Tr. Also known as spur.

The trace of a linear transformation on a finite-dimensional vector space is the trace (in the sense of the first definition) of the matrix associated with it.

One of the curves along which a given surface cuts a coordinate plane.

A point at which a given straight line in space passes through a coordinate plane. Also known as piercing point.

The projection of a given straight line in space on a coordinate plane.

(meteorology)

A precipitation of less than 0.005 inch (0.127 millimeter).

(science and technology)

An extremely small but detectable quantity of a substance.

## trace

The line appearing on the face of a cathoderay tube when the visible dot repeatedly sweeps across the face of the tube as a result of deflections of the electrons. The path of the dot from the end of one sweep to the start of the next sweep is called a

*retrace*. If more than one trace is shown on the same scope, the traces may be called an*A-trace, B-trace*, etc.