the bottom or base of anything; the part on which something stands or rests.

anything upon which something is based; fundamental principle; groundwork.

the principal constituent; fundamental ingredient.

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.

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.

noun

base , bed , bottom , foot , footing , ground , groundwork , rest , resting place , seat , substructure , support , antecedent , assumption , authority , axiom , backbone , background , backing , bedrock , cause , center , chief ingredient , core , crux , data , dictum , essence , essential , evidence , explanation , fundamental , hard fact , heart , infrastructure , justification , keynote , keystone , law , nexus , nucleus , postulate , premise , presumption , presupposition , principal element , principle , proof , reason , root , rudiment , sanction , security , source , substratum , theorem , theory , underpinning , warrant , foundation , fundament , status , term , cornerstone , motive