Nonsquare

Nonsquare is an adjective used to describe something that is not square. The term is common in mathematics, geometry, and linear algebra, and may be written as non-square or nonsquare depending on style. While non-square is the widely accepted form in many contexts, some technical texts use the closed compound nonsquare.

In arithmetic, a perfect square is an integer equal to k^2 for some integer k. Numbers that are not perfect squares are called nonsquare numbers or non-square integers. They do not equal the square of any integer. Examples include 2, 3, 5, 6, 7, 8, 10, and 12.

In geometry, a nonsquare refers to any figure that is not a square. Most quadrilaterals are nonsquares. A non-square rectangle, for instance, has unequal side lengths, while a square has all sides equal and angles of 90 degrees.

In linear algebra, a nonsquare matrix has a different number of rows and columns (m ≠ n). Such matrices are not invertible in the usual square-matrix sense, but they can have full row or column rank and are central to many applications, including solving linear systems and representing linear transformations.

Usage notes: hyphenation and capitalization vary by style guide. In mathematical writing, both "non-square" and "nonsquare" may appear, but the hyphenated form is often preferred in general prose, while the closed form appears in programming identifiers or specialized texts.

See also: Square number; Non-square (disambiguation); Non-square matrix; Rectangle; Geometry; Linear algebra.