The vector cross product from an algebraic point of view

Götz Trenkler

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 67-82
  • ISSN: 1509-9415

Abstract

top
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.

How to cite

top

Götz Trenkler. "The vector cross product from an algebraic point of view." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 67-82. <http://eudml.org/doc/287742>.

@article{GötzTrenkler2001,
abstract = {The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.},
author = {Götz Trenkler},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {vector cross product; generalized inverse; Moore-Penrose inverse; linear equations; vector algebras; eigenvalues; eigenspaces; generalized matrix inverse},
language = {eng},
number = {1},
pages = {67-82},
title = {The vector cross product from an algebraic point of view},
url = {http://eudml.org/doc/287742},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Götz Trenkler
TI - The vector cross product from an algebraic point of view
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 67
EP - 82
AB - The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
LA - eng
KW - vector cross product; generalized inverse; Moore-Penrose inverse; linear equations; vector algebras; eigenvalues; eigenspaces; generalized matrix inverse
UR - http://eudml.org/doc/287742
ER -

References

top
  1. [1] A. Ben-Israel, and T.N.E. Greville, Generalized Inverses: Theory and Applications, John Wiley & Sons, New York 1974. Zbl0305.15001
  2. [2] L.G. Chambers, A Course in Vector Analysis, Chapman and Hall, London 1969. 
  3. [3] B. Hague, An Introduction to Vector Analysis for Physicists and Engineers, (6th edition, revised by D. Martin), Methuen & Science Paperbacks, London 1970. 
  4. [4] T. Lancaster, and M. Tismenetsky, The Theory of Matrices. Academic Press, New York 1985. Zbl0558.15001
  5. [5] E.A. Milne, Vectorial Mechanics, Methuen & Co. Ltd., London 1965. 
  6. [6] C.R. Rao, and S.K. Mitra, Generalized Inverse of Matrices and its Applications, John Wiley & Sons, New York 1971. Zbl0236.15004
  7. [7] T.G. Room, The composition of rotations in Euclidean three-space, Amer. Math. Monthly 59 (1952), 688-692. Zbl0047.15001

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.