What does unitary mean?
Unitary describes something that forms one complete whole rather than a collection of independent parts. This sense is especially common in political and institutional contexts: a unitary state has a single central authority, while a federal state divides authority among constituent regions. In mathematics and physics, a unitary transformation preserves the structure of the space on which it acts. In linear algebra and quantum mechanics, this means preserving inner products, and consequently lengths and angles, even though the transformation may move vectors to different positions. The word is also used as a noun for a unitary transformation or matrix. Overall, unitary is more formal than simple, single, or whole, and it suggests both completeness and structural integrity. Its specialized mathematical meaning is precise but comparatively accessible because it expresses the idea of transformation without loss of geometric relationships.
Forming or constituting one complete whole; unified. In mathematics and physics, relating to a transformation that preserves inner products, lengths, and angles.
"The transformation is unitary because it preserves the inner product of every pair of vectors."
The general and political senses are formal, while the mathematical sense is technical.
A mathematical or physical transformation that preserves the relevant structure, especially inner products.
"Identity is the simplest unitary."
This noun is used mainly in mathematics, linear algebra, and quantum mechanics.
Rare in general prose and used mainly in mathematics for unitary transformations or matrices.
"The tensor product of two unitaries is itself unitary."
A unitary transformation does not necessarily leave points where they are; it leaves lengths and angles unchanged.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does unitary come from?
English unitary was formed from the Latin unitas, meaning “unity” or “oneness,” with the suffix -ary. The word entered English in the early nineteenth century and was later extended to mathematics and physics, where it describes transformations that preserve a particular structure. Its related English words include unit, unity, and unite, all reflecting the same Latin foundation of being one.
Related word forms
How unitary is actually used
The general and political senses are formal. The mathematical and quantum-mechanical senses are technical: a unitary transformation preserves inner products and therefore also preserves lengths and angles. Pronunciation varies between a British /ə/ sound and an American /ɛ/ sound in the final syllable.
Easily confused with unitary
Unity is the state or quality of being united, whereas unitary describes something constituted as one unified whole.