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Annihilating Polynomial
A polynomial ''P'' is ''annihilating'' or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of the linear operator or a matrix ''A'' evaluates to zero, i.e., is such that ''P(A) = 0''. Note that all characteristic polynomials and minimal polynomials of ''A'' are annihilating polynomials. In fact, every annihilating polynomial is the multiple of the minimal polynomial of an operator ''A''.Hoffman, K., Kunze, R., "Linear Algebra", 2nd ed., 1971, Prentice-Hall. (Definition on page 191 of section 6.3) See also * Cayley–Hamilton theorem * Minimal polynomial (linear algebra) Minimal may refer to: * Minimal (music genre), art music that employs limited or minimal musical materials * "Minimal" (song), 2006 song by Pet Shop Boys * Minimal (supermarket) or miniMAL, a former supermarket chain in Germany and Poland * Mini ... References {{reflist Matrix theory Polynomials Linear algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
