Eigenvalues of a Linear Transformation

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

The article presents well known facts about eigenvalues of linear transformation of a vector space (see [13]). I formalize main dependencies between eigenvalues and the diagram of the matrix of a linear transformation over a finite-dimensional vector space. Finally, I formalize the subspace [...] called a generalized eigenspace for the eigenvalue λ and show its basic properties.MML identifier: VECTSP11, version: 7.9.03 4.108.1028

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 4
• Strony: 289-295

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Karol Pąk

• Institute of Computer Science, University of Białystok, Poland

Bibliografia

• [1] Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137-142, 2007.
• [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [4] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992.
• [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [6] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
• [7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
• [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [13] I.N. Herstein and David J. Winter. Matrix Theory and Linear Algebra. Macmillan, 1988.
• [14] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
• [15] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• [16] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
• [17] Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001.
• [18] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.
• [19] Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001.
• [20] Michał Muzalewski. Rings and modules - part II. Formalized Mathematics, 2(4):579-585, 1991.
• [21] Michał Muzalewski and Lesław W. Szczerba. Construction of finite sequences over ring and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):97-104, 1991.
• [22] Karol Pαk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007.
• [23] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007.
• [24] Karol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269-275, 2008.
• [25] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• [26] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
• [27] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• [28] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990.
• [29] Wojciech A. Trybulec. Operations on subspaces in vector space. Formalized Mathematics, 1(5):871-876, 1990.
• [30] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990.
• [31] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [32] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.
• [33] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [34] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• [35] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.

Identyfikatory

DOI

10.2478/v10037-008-0035-x