# 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.
References in classic literature ?
One of them, with both elbows on the table, and a pen in her hand, was tracing characters upon a sheet of fine Dutch paper; the other, kneeling upon a chair, which allowed her to advance her head and bust over the back of it to the middle of the table, was watching her companion as she wrote, or rather hesitated to write.
And he told stories, tracing with a finger in the dust, of the immense and sumptuous ritual of avalanche-guarded cathedrals; of processions and devil-dances; of the changing of monks and nuns into swine; of holy cities fifteen thousand feet in the air; of intrigue between monastery and monastery; of voices among the hills, and of that mysterious mirage that dances on dry snow.
Then there is a sort of mathematical question," went on Fisher, leaning back in his limp way and looking up at the bare walls, as if tracing imaginary diagrams there.
Well, if our conjecture is correct and the girl's name is or was Sophy Kratides, we should have no difficulty in tracing her.
His own investigations had begun on a day in the preceding spring when, having been engaged in tracing the vicissitudes of the d'Urberville family, he had observed Durbeyfield's name on his waggon, and had thereupon been led to make inquiries about his father and grandfather till he had no doubt on the subject.
The Kangaroo immediately adjourned, tracing against the sunset sky a parabolic curve spanning seven provinces, and evanished below the horizon.
Then by means of the Myth of Pandora the poet shows how evil and the need for work first arose, and goes on to describe the Five Ages of the World, tracing the gradual increase in evil, and emphasizing the present miserable condition of the world, a condition in which struggle is inevitable.
whereas the truth-finder, having raked out that jakes, his own mind, and being there capable of tracing no ray of divinity, nor anything virtuous or good, or lovely, or loving, very fairly, honestly, and logically concludes that no such things exist in the whole creation.
While much had been done in England in tracing the course of evolution in nature, history, economics, morals and religion, little had been done in tracing the development of thought on these subjects.
I did not despair of still finding that evidence, and I had lost none of my anxiety to discover it, for I had lost none of my interest in tracing the father of the poor creature who now lay at rest in Mrs.
Torres, Special Agent in Charge of the Los Angeles Field Division of the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF), announces the release of aggregate trace data for crime guns submitted to ATF for tracing for calendar year 2010.
Although tracing African American stories presents its own challenges, many books, Internet sources and professional genealogists have sprung up to help you in your search.

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