What are matrix transformations?

  • Context: High School 
  • Thread starter Thread starter Sreekar adithya
  • Start date Start date
  • Tags Tags
    Matrix Transformations
Click For Summary

Discussion Overview

The discussion centers around the concept of matrix transformations, exploring their definitions, applications, and potential ambiguities in terminology. Participants examine the relationship between matrices and linear mappings, as well as the implications of changing matrices under different contexts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants assert that a matrix corresponds to a linear mapping between finite dimensional vector spaces, with applications such as modeling rotations or reflections.
  • Others emphasize that a matrix describes or represents a transformation, which is a common interpretation of the term "matrix transformation."
  • A participant raises a question about the original poster's intent, suggesting that clarification is needed on whether they refer to the linear transformation defined by the matrix or the transformation of the matrix itself, such as changing it to another matrix through a change of bases.

Areas of Agreement / Disagreement

Participants express differing interpretations of what is meant by "matrix transformation," indicating that multiple competing views remain regarding the terminology and its implications.

Contextual Notes

The discussion highlights potential ambiguities in the definitions of matrix transformations and the need for clarity on specific terms used, such as linear transformations versus changes of matrices.

Sreekar adithya
Messages
4
Reaction score
0
TL;DR
Quick understanding of transformation of an matrix
What does a transformation of a matrix means and how it could be used?
 
Physics news on Phys.org
A matrix corresponds to a linear mapping between (finite dimensional) vector spaces. It can for example be used to model rotations or reflections. Here is a video that explains it better than I ever could:

 
  • Like
  • Informative
Likes   Reactions: Sreekar adithya, WWGD, Ishika_96_sparkles and 2 others
Like QED said, repeating because I think it is an important point in avoiding confusion. A matrix describes or represents a transformation, that is what is usually meant by a matrix transformation.
 
we might need more info from the OP, as to whether he means the linear transformation defined by the matrix, or the transformation of the matrix, i.e.changing it to some other matrix, defined by a change of bases, say.
 
  • Like
Likes   Reactions: Delta2 and Sreekar adithya

Similar threads

Graduate Similarity transformation changing the determinant to 1
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Dimension of a Linear Transformation Matrix
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • · Replies 12 ·
Replies
12
Views
5K
Undergrad Orthogonal transformations preserve length
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Transform a 2x2 matrix into an anti-symmetric matrix
  • · Replies 5 ·
Replies
5
Views
2K
MHB Matrix Transforms: nxm, n->m, m->n, n+m->n/m
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Similarity transformation, basis change and orthogonality
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Is There a Connection Between Conjugation and Change of Basis?
  • · Replies 1 ·
Replies
1
Views
3K