Block Diagonal Matrices

Karol Pąk

Formalized Mathematics (2008)

  • Volume: 16, Issue: 3, page 259-267
  • ISSN: 1426-2630

Abstract

top
In this paper I present basic properties of block diagonal matrices over a set. In my approach the finite sequence of matrices in a block diagonal matrix is not restricted to square matrices. Moreover, the off-diagonal blocks need not be zero matrices, but also with another arbitrary fixed value.

How to cite

top

Karol Pąk. "Block Diagonal Matrices." Formalized Mathematics 16.3 (2008): 259-267. <http://eudml.org/doc/266911>.

@article{KarolPąk2008,
abstract = {In this paper I present basic properties of block diagonal matrices over a set. In my approach the finite sequence of matrices in a block diagonal matrix is not restricted to square matrices. Moreover, the off-diagonal blocks need not be zero matrices, but also with another arbitrary fixed value.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {259-267},
title = {Block Diagonal Matrices},
url = {http://eudml.org/doc/266911},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Karol Pąk
TI - Block Diagonal Matrices
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 3
SP - 259
EP - 267
AB - In this paper I present basic properties of block diagonal matrices over a set. In my approach the finite sequence of matrices in a block diagonal matrix is not restricted to square matrices. Moreover, the off-diagonal blocks need not be zero matrices, but also with another arbitrary fixed value.
LA - eng
UR - http://eudml.org/doc/266911
ER -

References

top
  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  4. [4] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990. 
  5. [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  6. [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  7. [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  8. [8] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991. 
  9. [9] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991. 
  10. [10] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4):573-577, 1997. 
  11. [11] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992. 
  12. [12] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  13. [13] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993. 
  14. [14] Karol Pαk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007. 
  15. [15] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007. 
  16. [16] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  17. [17] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  18. [18] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991. 
  19. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  20. [20] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992. 
  21. [21] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.