Eigenvalues of a Linear Transformation
Karol Pąk
Formalized Mathematics, Tome 16 (2008), p. 289-295 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267094 
@article{bwmeta1.element.doi-10_2478_v10037-008-0035-x,
     author = {Karol P\k ak},
     title = {Eigenvalues of a Linear Transformation},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {289-295},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0035-x}
}

Karol Pąk. Eigenvalues of a Linear Transformation. Formalized Mathematics, Tome 16 (2008) pp. 289-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0035-x/

[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. | Zbl 06213858

[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. | Zbl 0704.15001

[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.