What does multilinear mean?
Multilinear is an adjective meaning that something involves more than one line or is linear in each of several variables separately. Its mathematical use is especially important: a multilinear function may not be linear when all its variables are considered together, but it behaves linearly with respect to each variable individually. This makes multilinear maps and models useful in geometry, tensor analysis, image processing, and statistical modelling. The word combines the Latin-derived prefix multi-, meaning “many,” with linear, meaning “consisting of lines.” Outside specialised mathematics and related technical fields, the term is relatively uncommon; “multidimensional” may be more appropriate when the intended idea is simply that something has several dimensions. Understanding the distinction is useful because multilinearity imposes a precise mathematical structure rather than merely indicating numerical complexity.
adjectiveInvolving or relating to more than one line. In mathematics, multilinear means linear in each of several variables separately.
- Relating to or involving more than one line.
- In mathematics, linear in each of several variables separately.
"The researchers used a multilinear model to examine how several factors interact."
"The map is based on a multilinear projection that preserves several straight-line relationships."
"Multilinear algebra provides a framework for studying maps that are linear in every input variable."
A multilinear expression can be nonlinear overall while remaining linear in each variable it contains.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does multilinear come from?
Multilinear was formed in English by combining the Latin-derived prefix multi-, meaning “many,” with linear, an adjective derived from Latin linearis, “consisting of lines.” The underlying lineare and linea are also ancestors of related English words such as alignment and collinear. In mathematical usage, the compound acquired its specific sense of being linear in each of several variables separately.
Related word forms
How multilinear is actually used
The term is primarily technical and mathematical. It is less common than 'multidimensional' in general contexts and should not be used as a substitute when no separate linearity in multiple variables is intended.
Easily confused with multilinear
Multilinear describes a function or relationship that is linear in each variable separately, whereas multidimensional simply describes something involving multiple dimensions.