plural bases
ˈbā-ˌsēz

1

**:**the bottom of something considered as its foundation

2

**:**the principal component of something

Fruit juice constitutes the basis of jelly.

3

a

**:**something on which something else is established or based

stories with little basis in reality

no legal basis for a new trial

still some basis for hope

selected on the basis of test scores

b

**:**an underlying condition or state of affairs

hired on a trial basis

He is on a first-name basis with his customers.

c

**:**a fixed pattern or system

meets with us on a regular basis [=regularly]

The department sends reports on a daily basis. [=every day]

4

**:**the basic principle

concepts that form the basis of the country's economic policies

5

**:**a set of linearly independent vectors (see vector entry 1 sense 1a) in a vector space such that any vector in the vector space can be expressed as a linear combination of them with appropriately chosen coefficients (see coefficient sense 1)

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Merriam-Webster unabridged
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