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

If Congress accurately reflected our nation on the basis of race, about 63 percent would be white, not 80 percent.

From The Daily Beast

We see the Southern segregationists who threatened his life and that of his family on an almost daily basis.

From The Daily Beast

Yet the email references the 1970s, “when police officers were ambushed and executed on a regular basis.”

From The Daily Beast

Removing choice is bullying and seems a horrid basis on which to anchor your relationship.

From The Daily Beast

So, I can deal with them on a daily basis, I know how it affects my body.

From The Daily Beast

The m relates it to the nares or humming tone (which is the basis of all resonance in the voice).

From Project Gutenberg

A resolute push for quite a short period now might reconstruct the entire basis of our collective human life.

From Project Gutenberg

At the present time, certainly, no thought has ever occurred to Germans that they would not go back to a gold basis.

From Project Gutenberg

But here in this little valley of the Kaw, he was cheered to see his race on a practical and sensible basis.

From Project Gutenberg

The relative quantity of labor embodied in each object is the basis of its value.

From Project Gutenberg

Related Words

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