Math Operators

Math operators define the basic operations that act on numbers and other math constructs. Typically, operators take one or two expressions as input and calculate a result as output. For two mathematicians to produce the result when given the same expression, the order of operations is defined so that the result is unambiguous.

Arithmetic

The basic arithmetic operators are addition, subtraction, multiplication, and division. Introduced in elementary mathematics, they describe ways to manipulate numbers. As the notion of a number becomes more complex, their definitions are expanded beyond discrete numbers and properties are introduced to make the concept of a number and operations more cohesive. For example, in algebra, the operators are expanded to work with fractions and partial numbers.

Addition

Addition is a basic operation in mathematics for combining two numbers together. It is a binary operation denoted with the plus symbol with an expression on the left and an expression on the right.

Subtraction

Subtraction is a basic arithmetic operation of taking away one number from another number.

Multiplication

Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.

Division

The division operator returns the result of dividing one number by another number.

Algebra

These operators in the algebra section build upon the previous operators in the arithmetic section and add a variety of operators used to express more complicated patterns that appear in mathematics. For example, the factorial operator represents the patterns found in combinations and permutations. Another example is the exponent and logarithm operators which describe exponential growth and decay.

Absolute Value

The absolute value operator returns the distance from zero on the number line of a number.

Square Root

Returns the square root of the provided expression.

Radical

The radical operator returns the n-th root of the provided expression. The radical operator is an alternative way of writing a fractional exponent.

Exponent

The exponentiation operator is a binary operator. The base is an expression or number that is being raised to some exponent. The exponent expression is denoted using superscript text.

Logarithm

Taking the logarithm of a number is the inverse operation of exponentiation. The subscript number is the base of the logarithm and the expression is the operand.

Factorial

The factorial operator is represented using the exclamation mark. The operator is unary, meaning that it only operates on one expression. The operator is useful when calculating combinations and permutations.

Modulus

The modulus operator returns the remainder of dividing the first expression by the second expression.

Summation

The summation operator is represented by the summation symbol ∑ and represents the operation of summing a sequence of expressions together.

Product

The product operator is represented by the ∏ (product) symbol and is used to represent the operation of multiplying a sequence of expressions together.

Linear Algebra

Linear algebra is a branch of mathematics that deals with vectors, vector spaces, linear transformations, and systems of linear equations. These operators act on vectors and matrices to produce results like transformations.

Vector Addition

Vector addition is the operation of adding two vectors together. Visually, the operation can be thought of as placing the two vectors "tip to tail" and drawing the resulting vector.

Cross Product

The cross product operates on two vectors and produces another vector as a result.

Magnitude

The magnitude (or length) of a vector gives a scalar representation of its size, irrespective of its direction.

Dot Product

The dot product of two vectors, also called the scalar product, produces a number which represents how aligned the vectors are with each other.

Matrix Multiplication

Matrix multiplication is a way to compose linear transformations. In order to multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Matrix Transpose

The transpose of a matrix is an operator which reflects a matrix across its diagonal.

Matrix Determinant

The determinant operator calculates a scalar value from a square matrix.

Calculus

These calculus operators define the basic operations such as finding the rate of change of a function or the area underneath a curve.

Limit

The limit operator describes the result of an expression as a variable approaches a value. The operator is used in calculus to formalize what mathematicians mean by approach.

Integral

An integral can be geometrically interpreted as the area under the curve of a function between the two points a and b. Integrals are a core operator in calculus and are used throughout physics and higher-level mathematics.

Derivative

The derivative is one of the main operators in calculus.