Virtual Labs

a: Second order partial derivatives of a function Explanation

Explanation

b: First order partial derivatives of vector functions Explanation

Explanation

c: Determinant of a matrix Explanation

Explanation

d: Gradient of a scalar function Explanation

Explanation

a:

\begin{bmatrix}2x & 1 \\ y & x\end{bmatrix}

Explanation

b:

\begin{bmatrix}x & y \\ 2x & 1\end{bmatrix}

Explanation

c:

\begin{bmatrix}2 & 1 \\ y & x\end{bmatrix}

Explanation

d:

\begin{bmatrix}2x & y \\ 1 & x\end{bmatrix}

Explanation

a:

n \times m

Explanation

b:

m \times n

Explanation

c:

n \times n

Explanation

d:

m \times m

Explanation

a: First order derivatives Explanation

Explanation

b: Second order partial derivatives Explanation

Explanation

c: Determinants of derivatives Explanation

Explanation

d: Integrals of functions Explanation

Explanation

a:

\begin{bmatrix}2 & 0 \\ 0 & 2\end{bmatrix}

Explanation

b:

\begin{bmatrix}x & y \\ y & x\end{bmatrix}

Explanation

c:

\begin{bmatrix}2x & 0 \\ 0 & 2y\end{bmatrix}

Explanation

d:

\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}

Explanation

Jacobian and Hessians