Section: Mathematical Operators
y = a .^ b
The result y depends on which of the following three situations applies to the arguments a and b:
a is a scalar, b is an arbitrary n-dimensional numerical array, in which case the output is a raised to the power of each element of b, and the output is the same size as b.
a is an n-dimensional numerical array, and b is a scalar, then the output is the same size as a, and is defined by each element of a raised to the power b.
a and b are both n-dimensional numerical arrays of \emph{the same size}. In this case, each element of the output is the corresponding element of a raised to the power defined by the corresponding element of b.
double type, and negative numbers raised to fractional powers can return complex values.
and the second form
and in the third form
--> a = 2 a = <int32> - size: [1 1] 2 --> b = 1:4 b = <int32> - size: [1 4] Columns 1 to 4 1 2 3 4 --> c = a.^b c = <double> - size: [1 4] Columns 1 to 4 2 4 8 16
The second case shows a vector raised to a scalar.
--> c = b.^a c = <double> - size: [1 4] Columns 1 to 4 1 4 9 16
The third case shows the most general use of the dot-power operator.
--> A = [1,2;3,2] A = <int32> - size: [2 2] Columns 1 to 2 1 2 3 2 --> B = [2,1.5;0.5,0.6] B = <double> - size: [2 2] Columns 1 to 2 2.0 1.5 0.5 0.6 --> C = A.^B C = <double> - size: [2 2] Columns 1 to 2 1.0000000000000000 2.8284271247461903 1.7320508075688772 1.5157165665103980