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Jacobian vs Gradient - What's the difference?

jacobian | gradient |

In calculus terms the difference between jacobian and gradient

is that jacobian is the determinant of such a matrix while gradient is 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
equivalently, the inclination to the X axis of the tangent to the curve of the graph.

jacobian

English

Adjective

(-)
    • The Jacobian matrix has partial derivatives as its entries.

    Noun

    (en noun)
  • (calculus) A Jacobian matrix or its associated operator.
  • (calculus) The determinant of such a matrix.

    • External links

    * (wikipedia "Jacobian") English eponyms

    gradient

    English

    Noun

    (en noun) (slope) (wikipedia gradient)
  • A slope or incline.
  • A rate of inclination or declination of a slope.
  • (calculus) 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
    equivalently, the inclination to the X axis of the tangent to the curve of the graph.
  • (science) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
  • (analysis) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field ?: ∇φ

    • Synonyms

    * (slope) hill, incline, ramp, slope * (in calculus) slope (of a line )

    Derived terms

    * gradient wind * ruling gradient * supergradient * temperature gradient

    Adjective

    (-)
  • Moving by steps; walking.
    • gradient automata
    (Wilkins)
  • Rising or descending by regular degrees of inclination.
    • the gradient line of a railroad
  • Adapted for walking, as the feet of certain birds.

    • Anagrams

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