The Direction/Multiply Function ×

Monadic Use On Floats And Integers

× is a monadic function that returns the signum, or sign of the argument.

When the argument is complex, × returns the argument divided by its magnitude.

× 0 1 ¯2 3

0 1 ¯1 1

Dyadic Use On Floats And Integers

× is a dyadic function that works in two ways.

If the rho of both sides is the same it performs zip-wise multiplication

If either side has a rho of [1] it multiplies the value by every value in the other.

Here are some examples:

1 2 × 3 4

3 8

and

1 2 3 4 5 × 33

33 66 99 132 165

and

2 × 333 444

666 888

Monadic Use On Complex Nos

In a real number the monadic × gives the direction (ie 1 or ¯1 depending on whether the number is positive or negative). It does the same for complex numbers. It takes a given complex number and rescales it so that is magnitude equals 1. Obviously it is in the complex plane. The magnitude here is the square root of 3 square and 4 squared which equals 5. So we divide each component by 5 to get a complex number pointing in the same direction but with a magnitude of 1:

× 3J4

0.6J0.8

Dyadic Use On Complex Nos

This is normal complex number multiplication:

2J3 × 4j5

¯7J22

Dyadic Mixed Use On Complex Nos And Real Numbers

This is the same as normal complex multiplication with the real no cast into a imaginary with zero imaginary component:

2 × 4j5

8J10

4j5 × 2

8J10