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- Cayley–Hamilton_theorem abstract "In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex field) satisfies its own characteristic equation.More precisely, if A is a given n×n matrix and In is the n×n identity matrix, then the characteristic polynomial of A is defined aswhere "det" is the determinant operation. Since the entries of the matrix are (linear or constant) polynomials in λ, the determinant is also an n-th order polynomial in λ. The Cayley–Hamilton theorem states that "substituting" the matrix A for λ in this polynomial results in the zero matrix, p(A) = 0 .The powers of A, obtained by substitution from powers of λ, are defined by repeated matrix multiplication; the constant term of p(λ) gives a multiple of the power A0, which power is defined as the identity matrix.The theorem allows An to be expressed as a linear combination of the lower matrix powers of A.When the ring is a field, the Cayley–Hamilton theorem is equivalent to the statement that the minimal polynomial of a square matrix divides its characteristic polynomial.".
- Cayley–Hamilton_theorem wikiPageID "173547".
- Cayley–Hamilton_theorem wikiPageRevisionID "605731073".
- Cayley–Hamilton_theorem bgcolor "#F9FFF7".
- Cayley–Hamilton_theorem borderColour "#0073CF".
- Cayley–Hamilton_theorem cellpadding "6".
- Cayley–Hamilton_theorem indent "::".
- Cayley–Hamilton_theorem last "Atiyah".
- Cayley–Hamilton_theorem last "MacDonald".
- Cayley–Hamilton_theorem loc "Prop. 2.4".
- Cayley–Hamilton_theorem year "1969".
- Cayley–Hamilton_theorem subject Category:Articles_containing_proofs.
- Cayley–Hamilton_theorem subject Category:Matrix_theory.
- Cayley–Hamilton_theorem subject Category:Theorems_in_linear_algebra.
- Cayley–Hamilton_theorem comment "In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex field) satisfies its own characteristic equation.More precisely, if A is a given n×n matrix and In is the n×n identity matrix, then the characteristic polynomial of A is defined aswhere "det" is the determinant operation.".
- Cayley–Hamilton_theorem label "Cayley–Hamilton theorem".
- Cayley–Hamilton_theorem label "Satz von Cayley-Hamilton".
- Cayley–Hamilton_theorem label "Stelling van Cayley-Hamilton".
- Cayley–Hamilton_theorem label "Teorema de Cayley-Hamilton".
- Cayley–Hamilton_theorem label "Teorema de Cayley-Hamilton".
- Cayley–Hamilton_theorem label "Teorema di Hamilton-Cayley".
- Cayley–Hamilton_theorem label "Théorème de Cayley-Hamilton".
- Cayley–Hamilton_theorem label "Twierdzenie Cayleya-Hamiltona".
- Cayley–Hamilton_theorem label "Теорема Гамильтона — Кэли".
- Cayley–Hamilton_theorem label "مبرهنة كايلي-هاميلتون".
- Cayley–Hamilton_theorem label "ケイリー・ハミルトンの定理".
- Cayley–Hamilton_theorem label "凱萊-哈密頓定理".
- Cayley–Hamilton_theorem sameAs Cayley%E2%80%93Hamilton_theorem.
- Cayley–Hamilton_theorem sameAs Cayleyho-Hamiltonova_věta.
- Cayley–Hamilton_theorem sameAs Satz_von_Cayley-Hamilton.
- Cayley–Hamilton_theorem sameAs Teorema_de_Cayley-Hamilton.
- Cayley–Hamilton_theorem sameAs Théorème_de_Cayley-Hamilton.
- Cayley–Hamilton_theorem sameAs Teorema_di_Hamilton-Cayley.
- Cayley–Hamilton_theorem sameAs ケイリー・ハミルトンの定理.
- Cayley–Hamilton_theorem sameAs 케일리-해밀턴_정리.
- Cayley–Hamilton_theorem sameAs Stelling_van_Cayley-Hamilton.
- Cayley–Hamilton_theorem sameAs Twierdzenie_Cayleya-Hamiltona.
- Cayley–Hamilton_theorem sameAs Teorema_de_Cayley-Hamilton.
- Cayley–Hamilton_theorem sameAs Q656772.
- Cayley–Hamilton_theorem sameAs Q656772.
- Cayley–Hamilton_theorem wasDerivedFrom Cayley–Hamilton_theorem?oldid=605731073.