Matrix Invariance: T:X->Y Explained

Thread starter indigojoker
Start date Sep 14, 2007
Tags

Invariance Matrix

AI Thread Summary

Matrix invariance under a transformation T, denoted as T:X->Y, means that the transformation does not change the matrix X, resulting in T(X) being equal to X. This indicates that all elements of X remain unchanged in Y, rather than being scalar multiples. Therefore, if a matrix is invariant under T, it retains its original values post-transformation. The concept emphasizes that invariance implies identity rather than proportionality. Understanding this principle is crucial for applications in linear algebra and related fields.

Sep 14, 2007

indigojoker

I just wanted to know say a matrix X is invariant under some transformation T.

So:
T:X->Y is invariant...

does that mean all the elements of X are the same as the elements of Y? Or is the elements in Y a scalar multiple of the elements in X?

Physics news on Phys.org

Sep 14, 2007

Dick

Science Advisor

Homework Helper

If a matrix (or anything else) is invariant under a transformation T, then T(X)=X. Period.

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

View full post »