Transpose of a matrix

  • Thread starter matqkks
  • Start date
  • #1
201
2

Main Question or Discussion Point

What is the geometric interpretation of the transpose of a matrix? Is there any physical significance of the matrix transpose?
 

Answers and Replies

  • #2
236
0
What is the geometric interpretation of the transpose of a matrix? Is there any physical significance of the matrix transpose?
In a finite-dimensional vector space, the dual space (the space of linear functionals) is isomorphic to the vector space, and if A is the matrix for a linear map from vector spaces V to W (with bases X and Y), then there is an induced linear map between the dual spaces W* to V* (w.r.t. the dual bases X* and Y*), whose matrix is the transpose of A. But I don't know what the physical or geometric intuition is, if any, for this relationship.
 

Related Threads on Transpose of a matrix

  • Last Post
Replies
1
Views
9K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
5K
Replies
4
Views
2K
  • Last Post
Replies
3
Views
347
Replies
5
Views
1K
  • Last Post
Replies
2
Views
6K
Replies
6
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
1
Views
1K
Top