square

A function that squares its argument.

Syntax

• square(x)

  • x is a number, vector, or matrix

Description

• If x is a number, square(x) is the square of x, equal to x⋅x = x^2.

• If v is a vector, square(v) is the dot product of v and itself, that is, v⋅v = (v|v) = norm(v)^2.

• If A is a square matrix, square(A) is the square of A, that is, A⋅A = A^2.

Notes

Typically, you write x^2 to square a number or matrix x. However, if you need the squaring operation as a function, square is more convenient to write than x ↦ x^2.

Examples

square(5)

25

square(❨3, 0, −2❩)

13

square(❨❨2, 1❩, ❨i, 3❩❩)

⎛4 + i   5  ⎞
⎝ 5⋅i  9 + i⎠

SequenceVector(20) @ square

(1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400)

SequenceVector(10) @ prime @ square

(4, 9, 25, 49, 121, 169, 289, 361, 529, 841)

See also

• sqr (synonym)

• sqrt