## Definition of basis

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

**:**the principal component of something

- Fruit juice constitutes the basis of jelly.

**:**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

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

- hired on a trial basis

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

**:**a fixed pattern or system

- meets with us on a regular basis [=regularly]

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

**:**the basic principle

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

**:**a set of linearly independent vectors (see

^{1}vector 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 1)