basis

[ bey-sis ]

noun

, plural ba·ses [bey, -seez].

1. the bottom or base of anything; the part on which something stands or rests.
2. anything upon which something is based; fundamental principle; groundwork.
3. the principal constituent; fundamental ingredient.
4. a basic fact, amount, standard, etc., used in making computations, reaching conclusions, or the like:

   The nurse is paid on an hourly basis. He was chosen on the basis of his college grades.

5. Mathematics. a set of linearly independent elements of a given vector space having the property that every element of the space can be written as a linear combination of the elements of the set.

basis

/ ˈbeɪsɪs /

noun

1. something that underlies, supports, or is essential to something else, esp an abstract idea
2. a principle on which something depends or from which something has issued
3. maths (of a vector space) a maximal set of linearly independent vectors, in terms of which all the elements of the space are uniquely expressible, and the number of which is the dimension of the space

   the vectors x, y and z form a basis of the 3-dimensional space all members of which can be written as ax + by + cz

basis

/ bā′sĭs /

, Plural bases bā′sēz′

1. A set of independent vectors whose linear combinations define a vector space, such as a reference frame used to establish a coordinate system.

Word History and Origins

Origin of basis¹

First recorded in 1525–35; from Latin, from Greek básis “step, place one stands on, pedestal,” from ba(ínein) “to walk, step” ( come ) + -sis -sis; base ¹

Word History and Origins

Origin of basis¹

C14: via Latin from Greek: step, from bainein to step, go

Idioms and Phrases

see on a first-name basis .

Synonym Study

See base ¹.

Example Sentences

Staff say the area has become dangerous and intimidating, and that despite reporting thefts to police on an almost daily basis, nothing has been done.

From BBC

"We are in contact with police on almost a daily basis at this point."

From BBC

A strident, even hysterical defender of Trump throughout his scandals, Gaetz asserted that the Jan. 6, 2021, insurrection — the basis for the largest prosecution in the history of the Justice Department — was the work of far-left agitators masquerading as Trump supporters.

From Los Angeles Times

Those reservations will be available on a first-come, first-served basis on www.recreation.gov beginning Monday at 8 a.m.

From Los Angeles Times

Mr Jones said the post had been advertised three times but so far it had "not been possible to make a permanent appointment" and arrangements to appoint a head teacher on a temporary basis were under way.

From BBC

Related Words

• assumption
• base
• essential
• evidence
• explanation
• footing
• fundamental
• justification
• premise
• principle
• proof
• reason
• security
• support
• theory