GT17.1. Permutation Matrices

Abstract Algebra: (Linear Algebra Required) The symmetric group S_n is realized as a matrix group using permutation matrices. That is, S_n is shown to the isomorphic to a subgroup of O(n), the group of nxn real orthogonal matrices. Applying Cayley's Theorem, we show that every finite group is isomorphic to a subgroup of O(n).

Category:

Education

Tags:

• Mathematics
• abstract
• algebra
• group
• theory
• symmetric
• permutation
• bijection
• isomorphism
• invertible
• orthogonal
• matrix
• determinant
• alternating
• cycle
• trace
• eigenvalue
• root
• unity

[MathDoctorBob]

@tw3ak1t You're welcome! Videos are no substitute for an actual teacher, so if you have questions, I'm happy to help. An important part of math is asking questions. - Bob

[tw3ak1t]

Thanks Dr Bob, I have very little tangible qualifications in Math, however I have a keen interest in research through self-studying. Your contributions are highly regarded and increasingly reflected to my interest in Math theoretical concepts.

Your teaching allows me to try - what is not tangible through traditional methods of education.