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homogeneous polynomial::noun | Spocien Dictionary
| Type | Words |
|---|---|
| Type of | multinomial, polynomial |
| Has types | quantic |
Examples of homogeneous polynomial
homogeneous polynomial
An algebraic form, or simply form, is another name for a homogeneous polynomial.
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Algebraic form, or simply form, is another term for homogeneous polynomial.
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Cayley introduced the idea of homogeneous polynomial forms, and more specifically quadratic forms, on projective space.
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A homogeneous polynomial of degree 0 is simply a scalar, while a homogeneous polynomial of degree 1 is a linear functional, also known as a covector.
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The idea of scale invariance of a monomial generalizes in higher dimensions to the idea of a homogeneous polynomial, and more generally to a homogeneous function.
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Polynomial rings and their quotients by homogeneous ideals are typical graded algebra.
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Thus, the graded algebras generated by elements of degree 1 are exactly, up to an isomorphism, the quotients of polynomial rings by homogeneous ideals.
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The ring R is a polynomial ring so is graded by degrees, and the ideal I is defined to be the ideal generated by the homogeneous invariants of positive degrees.
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