Define Jacobian.
Understand the Problem
The question is asking for the definition of the term 'Jacobian', which refers to a concept in mathematics, specifically in the context of multivariable calculus. It typically relates to the matrix of all first-order partial derivatives of a vector-valued function.
Answer
The Jacobian is a matrix of all first-order partial derivatives of a vector-valued function.
In vector calculus, the Jacobian is a matrix of all first-order partial derivatives of a vector-valued function. It plays a crucial role in multivariable calculus, particularly in transformations and computing gradients.
Answer for screen readers
In vector calculus, the Jacobian is a matrix of all first-order partial derivatives of a vector-valued function. It plays a crucial role in multivariable calculus, particularly in transformations and computing gradients.
More Information
The Jacobian matrix can be used to determine the local behavior of functions, including rotations, scaling, and shearing effects within transformations.
Sources
- Jacobian Matrix - Wikipedia - en.wikipedia.org
- Understanding the Jacobian matrix - Khan Academy - khanacademy.org
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