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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Jacobian and Hessians

Choose difficulty:

Beginner

Intermediate

Advanced

If

f(x,y) = xy

, what is

\frac{\partial^2 f}{\partial x \partial y}

?

a:

0

Explanation

Explanation

b:

1

Explanation

Explanation

c:

x

Explanation

Explanation

d:

y

Explanation

Explanation

The Hessian matrix of a function

f: \mathbb{R}^n \rightarrow \mathbb{R}

is of size:

a:

n \times 1

Explanation

Explanation

b:

1 \times n

Explanation

Explanation

c:

n \times n

Explanation

Explanation

d:

m \times n

Explanation

Explanation

Which of the following is true about the Hessian matrix (for well-behaved functions)?

a: It is always triangular Explanation

Explanation

b: It is symmetric Explanation

Explanation

c: It is diagonal Explanation

Explanation

d: It is zero Explanation

Explanation

The Jacobian determinant is commonly used in:

a: Optimization Explanation

Explanation

b: Coordinate transformations Explanation

Explanation

c: Differential equations only Explanation

Explanation

d: Matrix multiplication Explanation

Explanation

For

F(x,y) = (x+y,\; x-y)

, what is the Jacobian determinant?

a:

0

Explanation

Explanation

b:

1

Explanation

Explanation

c:

-2

Explanation

Explanation

d:

-1

Explanation

Explanation

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