VECTOR-VALUED MULTIVARIABLE FUNCTIONS

A function $f:D \rightarrow ℝ^m$ is a vector valued multivariable function iff $D \subseteq ℝ^n$, where $n>1$ and $m>1$.

• At least 2 parameters as input
• The output is an element of $ℝ^m$, where $m>1$

Some linear transformations are also vector-valued multivariable functions. Examples:

• $T(x,y,z)=(x+y,y-z,z-x+y)$
• $T(x,y)=(y,x)$

Other examples:

• $f(x,y,z)=(e^x,e^y,\ln(z))$
• $f(x,y)=(x^2+\cos(y),\frac{xy}{x^2+y^2})$