GT17.1. Permutation Matrices

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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).

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permutation matrix P is obtained from the identity matrix I by some permutation of rows (or columns). Show that P^-1 = P^T

АсылжанБазарбай-гз
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@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


MathDoctorBob
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Thank you for your awesome videos! What would happen if a group G would be infinite? Can it be realised as a subgroup of an orthogonal matrix group, with matrices of infinite dimension? 

asmallmind
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Why must the permutation matrix always have an inverse?

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