# trace

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## 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 = a11 + a22 + … + ann

If the characteristic equation of A has the roots (called eigenvalues or characteristic roots) λ1, λ2,…,λn, then

Tr A = λ1 + λ2 + …. + λn

## 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.
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