Contents Previous Next Subchapters Current Chapters-> positive negative addition coercion subtraction multiplication division equality ordered logicalOperator matrixMultiplication matrixDivision exponentiation transpose norm stringEquality stringOrdered sequence operationOrder Parent Chapters-> Omatrix6 expression exponentiation Search Tools-> contents reference index search

Element-By-Element Exponentiation
 Syntax base` ^ `exponent See Also multiplication , division

Description
Element-by-element exponentiation of base to exponent, where base and exponent are integer, real, double-precision, or complex. (One, but not both, of the values may be logical.)

Tutorial

Scalar Exponentiation
If you enter ```      6^2 ``` O-Matrix will respond ```      36 ```
Exponentiation by a Matrices
If you enter ```      x = {[1, 2, 3], [4, 5, 6]}      y = {[2, 2, 2], [2, 2, 2]}      x^y ``` O-Matrix will print ```      {      [ 1 , 4 , 9 ]      [ 16 , 25 , 36 ]      } ```
Exponentiation by a Scalar
If you enter ```      x = {[1, 2, 3], [4, 5, 6]}      x^2 ``` O-Matrix will respond ```      {      [ 1 , 4 , 9 ]      [ 16 , 25 , 36 ]      } ```
Exponentiation of a Scalar
If you enter ```      x = {[1, 2, 3], [4, 5, 6]}      2^x ``` O-Matrix will respond ```      {      [ 2 , 4 , 8 ]      [ 16 , 32 , 64]      } ```
Reference
If the value types do not agree, O-Matrix will coerce the values as detailed in the coercion table. ``` ```Exponentiation to a fractional power can be ambiguous. For example, both `i` and `-i` are square roots of `-1`. O-Matrix uses a polar representation of the base when performing complex exponentiation. ``` ```Suppose that `z` is a complex base and w is a real exponent. O-Matrix expresses `z` as ```             i theta      z = r e ```where `r` is real and `-pi < theta < pi`. The result is defined by ```       w    w  i theta w      z  = r  e ```