− (minus)

The minus sign is used for several different operations on various kinds of operands and has two distinct syntactic forms:

As a binary operator, − is typically used for mathematical subtraction.
As a unary operator, − is typically used to denote the opposite number, vector, or matrix.

Syntax

a − b
- applicable to several different kinds of operands a and b
−a
- a is a number, vector, or matrix

Description and examples

Binary operator: subtraction

Subtraction of numbers

If a and b are numbers (integers, rational numbers, real number, or complex numbers), a − b is the mathematical difference of a and b. The type of the difference is the most specific type possible.

Some examples:

If a and b are both integers, so is a − b if no integer overflow occurs; in that case, the result is a real number.
If a is an integer and b a rational number, a − b is a rational number.
If a is an integer and b a real number, a − b is a real number.
If a is an integer and b a complex number, a − b is a complex number.
If a is a real number and b a complex number, a − b is a complex number.
If a is a rational number and b a complex number, a − b is a complex number.

π − e

0.423310825131

3/7 − 2/5

1/35	(=0.0285714285714)

Vector subtraction

If u and v are vectors, u − v is the vector difference between u and v. u − v is a complex vector if at least one of u and v is complex; otherwise, u − v is a real vector.

u and v must be of the same dimension.

u ≔ ❨2, 1, 3❩; v ≔ ❨0, 2, 1❩; u − v

 ⎛2 ⎞
e⎜−1⎟
 ⎝2 ⎠

Matrix subtraction

If A and B are matrices, A − B is the matrix difference between A and B. A − B is a complex matrix if at least one of A and B is complex; otherwise, A − B is a real matrix.

A and B must be of the same size.

A ≔ ❨❨1, 3❩, ❨−i, 1❩❩; B ≔ ❨❨2, 1❩, ❨0, −1❩❩; A − B

⎛−1   2⎞
⎝−i   2⎠

Subtracting a scalar from a vector

If v is a vector and x a number, then v − x is the vector obtained from v by subtracting x from each component. If either v or x is complex, v − x is a complex vector. Otherwise, v − x is a real vector.

❨1, 5, 2❩ − i

 ⎛1 − i⎞
e⎜5 − i⎟
 ⎝2 − i⎠

Subtracting a scalar from a matrix

If A is a matrix and x a number, then A − x is the matrix obtained from A by subtracting x from each entry. If either A or x is complex, A − x is a complex matrix. Otherwise, A − x is a real matrix.

ZeroMatrix(4) − 1

⎛−1  −1  −1  −1⎞
⎜−1  −1  −1  −1⎟
⎜−1  −1  −1  −1⎟
⎝−1  −1  −1  −1⎠

Superposing two sounds by samplewise subtraction

If s and t are two sounds, s − t is the superposed sound obtained by samplewise subtraction.

SineTone(100, 0.1, 1) − SineTone(400, 0.1, 1)

A 1-second 32-bit 48000 Hz 1-channel sound.

SineTone(100, 0.1, 1) − SineTone(100, 0.1, 1)

A 1-second 32-bit 48000 Hz 1-channel sound.

SoundMax(ans)

Unary operator

If x is a number, vector, or matrix, −x is the opposite number, vector, or matrix, that is, 0 − x where 0 stands for the suitable zero object.

−π

−3.14159265359	(=−π)

−❨1, 0, 0❩

 ⎛−1⎞
e⎜0 ⎟
 ⎝0 ⎠

−IdentityMatrix(3)

⎛−1   0   0⎞
⎜ 0  −1   0⎟
⎝ 0   0  −1⎠

Notes

The binary operator − is mapped to the subtract function.
The unary operator − is mapped to the negative function.