basis
nounDefinition of basis
1
: the bottom of something considered as its foundation
2
: the principal component of something
Fruit juice constitutes the basis of jelly.
3a
: 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 firstname 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
mathematics
: 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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