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Where does the Jacobian Matrix come from? 2 different answers/perspectives

This video uses some standard methods of vector calculus and some standard methods of linear algebra to give some motivation for why the Jacobian works and where it comes from. Enjoy!

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67 - The geometric meaning of J
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67 - The geometric meaning of J

Gradients, Hessians, and All Those Derivative Tests
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Gradients, Hessians, and All Those Derivative Tests

The Jacobian Determinant
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The Jacobian Determinant

Best Explanation of Jacobian and Change of Variables
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Best Explanation of Jacobian and Change of Variables

What is Jacobian? | The right way of thinking derivatives and integrals
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What is Jacobian? | The right way of thinking derivatives and integrals

The Jacobian Matrix
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The Jacobian Matrix

Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
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Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

Change of Variables and the Jacobian
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Change of Variables and the Jacobian

Jacobian prerequisite knowledge
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Jacobian prerequisite knowledge

Why is there an extra "r" in dxdy=rdrdθ? (geometry vs Jacobian)
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Why is there an extra "r" in dxdy=rdrdθ? (geometry vs Jacobian)

Oxford Calculus: Jacobians Explained
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Oxford Calculus: Jacobians Explained

Researchers thought this was a bug (Borwein integrals)
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Researchers thought this was a bug (Borwein integrals)

The Obsessive Engineering of Precision Linear Motion
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The Obsessive Engineering of Precision Linear Motion

Calculus without Coordinates! (Exploring the Exotic Exterior Derivative P.1)
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Calculus without Coordinates! (Exploring the Exotic Exterior Derivative P.1)

Multivariable Calculus | The Jacobian
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Multivariable Calculus | The Jacobian

Understanding Lagrange Multipliers Visually
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Understanding Lagrange Multipliers Visually

The Jacobian matrix
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The Jacobian matrix

The Professor Who Taught People How To Think (1962)
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The Professor Who Taught People How To Think (1962)

32. Jacobian Change of Variables (Proof)
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32. Jacobian Change of Variables (Proof)

Weird spaces where π = 4
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Weird spaces where π = 4

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