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The same vector can be represented in two different bases (purple and red arrows). In mathematics, a set B of vectors in a vector space V is called a basis (pl.: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B.
bases / ˈ b eɪ s ɪ z / noun plural of base / ˈ b eɪ s iː z / noun plural of basis: bass / ˈ b eɪ s / noun low in pitch / ˈ b æ s / noun a fish blessed / ˈ b l ɛ s ɪ d / adjective having divine aid / ˈ b l ɛ s t / verb past tense of bless: bow / ˈ b oʊ / noun a stringed weapon, or the initiator of sound in some stringed musical ...
Bases may refer to: Bases (fashion), a military style of dress adopted by the chivalry of the sixteenth century; Business Association of Stanford Entrepreneurial Students (BASES) the plural form of base (disambiguation) the plural form of basis (disambiguation)
where "old" and "new" refer respectively to the initially defined basis and the other basis, and are the column vectors of the coordinates of the same vector on the two bases. A {\displaystyle A} is the change-of-basis matrix (also called transition matrix ), which is the matrix whose columns are the coordinates of the new basis vectors on the ...
Gröbner bases are primarily defined for ideals in a polynomial ring = [, …,] over a field K.Although the theory works for any field, most Gröbner basis computations are done either when K is the field of rationals or the integers modulo a prime number.
In mathematics, a base (or basis; pl.: bases) for the topology τ of a topological space (X, τ) is a family of open subsets of X such that every open set of the topology is equal to the union of some sub-family of .
Before him, former President Donald Trump — who will soon take office again — spent Christmases in Florida at his Mar-a-Lago estate, per reports.During their holidays in Florida, Trump and ...
A plural base title can also redirect to an article (Bookends redirects to Bookend; Faces redirects to Face). If separate primary topics are determined, add a hatnote from the plural page to the singular form (or vice versa). Sometimes, what appears to be a plural form may also be a separate word, which can influence the primary topic decision.