Get to know Jacobian better with 10+ real example sentences, the meaning.
Jacobian in a sentence
Jacobian meaning
Used to specify certain mathematical objects named in honour of C. G. J. Jacobi.
Using Jacobian
- The main meaning on this page is: Used to specify certain mathematical objects named in honour of C. G. J. Jacobi.
- In the example corpus, jacobian often appears in combinations such as: the jacobian, jacobian matrix, jacobian determinant.
Context around Jacobian
- Average sentence length in these examples: 25.2 words
- Position in the sentence: 5 start, 7 middle, 1 end
- Sentence types: 13 statements, 0 questions, 0 exclamations
Corpus analysis for Jacobian
- In this selection, "jacobian" usually appears in the middle of the sentence. The average example has 25.2 words, and this corpus slice is mostly made up of statements.
- Around the word, matrix, determinant and morgan stand out and add context to how "jacobian" is used.
- Recognizable usage signals include called the jacobian is useful and denotes the jacobian matrix of. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "jacobian" sits close to words such as aaronson, abai and abass, which helps place it inside the broader word index.
Example types with jacobian
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
This so-called Jacobian matrix is often used for explicit computations. (11 words)
Canton scored its final points of the night when Jacobian Morgan ran in from two yards out. (17 words)
The Jacobian matrix reduces to a 1×1 matrix whose only entry is the derivative f (x). (17 words)
While locally the more general transformation law can indeed be used to recognise these tensors, there is a global question that arises, reflecting that in the transformation law one may write either the Jacobian determinant, or its absolute value. (39 words)
From this perspective the chain rule therefore says: : or for short, : That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points). (34 words)
If ƒ is differentiable, this is equivalent to: : where J(x) denotes the Jacobian matrix of partial derivatives of ƒ at x and is the induced norm on the matrix. (30 words)
Example sentences (13)
The backups are freshmen Dillon Markiewicz and JaCobian Morgan, who played briefly against Clemson, his first action in college.
Canton scored its final points of the night when Jacobian Morgan ran in from two yards out.
A quantity called the Jacobian is useful for studying functions when both the domain and range of the function are multivariable, such as a change of variables during integration.
From this perspective the chain rule therefore says: : or for short, : That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points).
If ƒ is differentiable, this is equivalent to: : where J(x) denotes the Jacobian matrix of partial derivatives of ƒ at x and is the induced norm on the matrix.
In this case, the above rule for Jacobian matrices is usually written as: : The chain rule for total derivatives implies a chain rule for partial derivatives.
Quasi-Newton methods When the Jacobian is unavailable or too expensive to compute at every iteration, a Quasi-Newton method can be used.
The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.
The Jacobian matrix reduces to a 1×1 matrix whose only entry is the derivative f (x).
This so-called Jacobian matrix is often used for explicit computations.
Volume and Jacobian determinant As pointed out above, the absolute value of the determinant of real vectors is equal to the volume of the parallelepiped spanned by those vectors.
We can also express this compactly using the Jacobian determinant : : This single equation together with appropriate boundary conditions describes 2D fluid flow, taking only kinematic viscosity as a parameter.
While locally the more general transformation law can indeed be used to recognise these tensors, there is a global question that arises, reflecting that in the transformation law one may write either the Jacobian determinant, or its absolute value.
Common combinations with jacobian
These word pairs occur most frequently in English texts: