# basis

< /ˈbeɪ siz/.

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.

noun plural -ses (-siːz)

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 spacethe vectors x, y and z form a basis of the 3-dimensional space all members of which can be written as a x + b y + c z
n.

1570s, “bottom or foundation (of something material),” from Latin basis “foundation,” from Greek basis “a step, stand, base, that whereon one stands,” from bainein “go, step” (see come). Transferred and figurative senses (of immaterial things) are from c.1600.

n. pl. ba•ses (-sēz′)

1. The foundation upon which something, such as an anatomical part, rests.

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.

see on a first-name basis.

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