Eigenvalues of a Linear Transformation

Karol Pąk

Formalized Mathematics (2008)

  • Volume: 16, Issue: 4, page 289-295
  • ISSN: 1426-2630

Abstract

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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

How to cite

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Karol Pąk. "Eigenvalues of a Linear Transformation." Formalized Mathematics 16.4 (2008): 289-295. <http://eudml.org/doc/267094>.

@article{KarolPąk2008,
abstract = {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},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {289-295},
title = {Eigenvalues of a Linear Transformation},
url = {http://eudml.org/doc/267094},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Karol Pąk
TI - Eigenvalues of a Linear Transformation
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 4
SP - 289
EP - 295
AB - 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
LA - eng
UR - http://eudml.org/doc/267094
ER -

References

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  1. [1] Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137-142, 2007. 
  2. [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  3. [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  4. [4] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992. 
  5. [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  6. [6] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990. 
  7. [7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  8. [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  9. [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  10. [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  11. [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  12. [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  13. [13] I.N. Herstein and David J. Winter. Matrix Theory and Linear Algebra. Macmillan, 1988. Zbl0704.15001
  14. [14] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991. 
  15. [15] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  16. [16] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996. 
  17. [17] Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001. 
  18. [18] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001. 
  19. [19] Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001. 
  20. [20] Michał Muzalewski. Rings and modules - part II. Formalized Mathematics, 2(4):579-585, 1991. 
  21. [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. [22] Karol Pαk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007. 
  23. [23] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007. 
  24. [24] Karol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269-275, 2008. 
  25. [25] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990. 
  26. [26] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990. 
  27. [27] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  28. [28] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990. 
  29. [29] Wojciech A. Trybulec. Operations on subspaces in vector space. Formalized Mathematics, 1(5):871-876, 1990. 
  30. [30] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990. 
  31. [31] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  32. [32] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991. 
  33. [33] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  34. [34] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  35. [35] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993. 

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