Definitions for gradient
ˈgreɪ di əntgra·di·ent

Princeton's WordNetRate this definition:4.0 / 3 votes

1. gradientnoun

   a graded change in the magnitude of some physical quantity or dimension

2. gradient, slopenoun

   the property possessed by a line or surface that departs from the horizontal

   "a five-degree gradient"

GCIDERate this definition:3.2 / 5 votes

1. Gradientnoun

   The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.4. (Chem., Biochem.) The variation of the concentration of a chemical substance in solution through some linear path; also called concentration gradient; -- usually measured in concentration units per unit distance. Concentration gradients are created naturally, e.g. by the diffusion of a substance from a point of high concentration toward regions of lower concentration within a body of liquid; in laboratory techniques they may be made artificially.

WiktionaryRate this definition:1.0 / 1 vote

1. gradientnoun

   A slope or incline.

2. gradientnoun

   A rate of inclination or declination of a slope.

3. gradientnoun

   Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x.

4. gradientnoun

   The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.

5. gradientnoun

   A vector operator that maps each value of a scalar field to a vector equal to the greatest rate of change of the scalar. Notation for a scalar field u03C6: u03C6

6. Etymology: From gradiens, present participle of gradi

Samuel Johnson's DictionaryRate this definition:0.0 / 0 votes

1. Gradientadjective

   Walking; moving by steps.

   Etymology: gradiens, Latin.

   Amongst those gradient automata, that iron spider is especially remarkable, which, being but of an ordinary bigness, did creep up and down as if it had been alive. John Wilkins.

WikipediaRate this definition:0.0 / 0 votes

1. Gradient

   In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point p, the direction of the gradient is the direction in which the function increases most quickly from p, and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f ( r ) {\displaystyle f({\bf {{r})}}} may be defined by:

ChatGPTRate this definition:0.0 / 0 votes

1. gradient

   Gradient, in mathematics and physics, generally refers to a rate of change or difference in a certain variable across space or distance. In the context of vector calculus, it is a vector operator that operates on a scalar function to produce a vector whose magnitude is the maximum rate of change of the function, and which is pointed in the direction of that maximum rate of change. In the context of machine learning and optimization, gradient refers to the slope of a function at a particular point, indicating the direction and rate of fastest increase of the function. It is often used in algorithms to find local or global minimum or maximum of a function.

Webster DictionaryRate this definition:4.0 / 1 vote

1. Gradientadjective

   moving by steps; walking; as, gradient automata

2. Gradientadjective

   rising or descending by regular degrees of inclination; as, the gradient line of a railroad

3. Gradientadjective

   adapted for walking, as the feet of certain birds

4. Gradientnoun

   the rate of regular or graded ascent or descent in a road; grade

5. Gradientnoun

   a part of a road which slopes upward or downward; a portion of a way not level; a grade

6. Gradientnoun

   the rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient

7. Etymology: [L. gradiens, p. pr. of gradi to step, to go. See Grade.]

WikidataRate this definition:0.0 / 0 votes

1. Gradient

   In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. In simple terms, the variation in space of any quantity can be represented by a slope. The gradient represents the steepness and direction of that slope. A generalization of the gradient for functions on a Euclidean space that have values in another Euclidean space is the Jacobian. A further generalization for a function from one Banach space to another is the Fréchet derivative.

Dictionary of Military and Associated TermsRate this definition:0.0 / 0 votes

1. gradient

   The rate of inclination to horizontal expressed as a ratio, such as 1:25, indicating a one unit rise to 25 units of horizontal distance.

Matched Categories

1. • Change
   • Position

Anagrams for gradient »

1. red giant

2. redating

3. treading

4. derating

How to pronounce gradient?

1. Alex

   US English

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Karen

   Australian

   Hayley

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   Priya

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   Neerja

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   Oliver

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How to say gradient in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of gradient in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of gradient in Pythagorean Numerology is: 6

Examples of gradient in a Sentence

1. Photographer Blincoe:

   You could take a photo of a bouquet of flowers or you could spend five hours clipping the tops and arranging them by gradient, it's just a different way of looking at something that other people aren't willing to put in the time for.

2. Sam Lillo:

   In general, the forecasts are showing ridging with above-normal temperatures in the South, cooler to the north, and that temperature gradient enhancing the jet stream across the center of the Sam Lillo.

3. The NWS:

   Snowfall totals are forecast to be over a foot for portions of the Northeast west of Interstate 95 through Thursday evening, the major cities will be on the gradient in between the substantial snowfall totals and light snowfall totals, so there is uncertainty in how much snow will fall in areas such as New York City.

4. James Rubin:

   What you see is a gradient, among the groups that were flooded, they had the greatest mental health problems.

5. Tinggui Wang:

   A white dwarf is a very compact star, as such, close to the star, the gradient of the gravitational field can be very large.

Popularity rank by frequency of use

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=gradient
2. ^ GCIDE
   https://gcide.gnu.org.ua/?q=gradient
3. ^ Wiktionary
   https://en.wiktionary.org/wiki/Gradient
4. ^ Samuel Johnson's Dictionary
   https://johnsonsdictionaryonline.com/views/search.php?term=gradient
5. ^ Wikipedia
   https://en.wikipedia.org/wiki/Gradient
6. ^ ChatGPT
   https://chat.openai.com
7. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/gradient
8. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=gradient
9. ^ Dictionary of Military and Associated Terms
   https://www.tradoc.army.mil/wp-content/uploads/2020/10/AD1029823-DOD-Dictionary-of-Military-and-Associated-Terms-2017.pdf