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PERMUTATION MATRICES AND PERMUTATION GROUPS - CSIR NET 2014 I PART B Q.22
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0:00 INTRO
01:26 PROBLEM STATEMENT.
01:27 DEFINITION OF A PERMUTATION.
01:55 DEFINITION OF A PERMUTATION MATRIX.
03:08 EXAMPLE OF A PERMUTATION MATRIX.
06:43 DIFFICULTIES IN WORKING WITH PERMUTATION MATRICES.
09:46 A BIJECTION BETWEEN PERMUTATIONS IN Sn AND PERMUTATION MATRICES OF ORDER n x n.
10:48 EQUIVALENT DEFINITION OF PERMUTATION MATRICES: EACH ROW AND COLUMN HAS EXACTLY ONE ONE.
11:55 ELEMENTS OF THE SYMMETRIC GROUP ON THREE SYMBOLS S3.
12:18 EXAMPLE: SET OF ALL 3 X 3 PERMUTATION MATRICES.
16:14 EXAMPLE OF A BIJECTION BETWEEN S3 AND THE SET OF ALL 3 X 3 PERMUTATION MATRICES.
17:04 BIJECTION BETWEEN SYMMETRIC GROUP ON n SYMBOLS AND THE SET OF ALL n X n PERMUTATION MATRICES.
17:42 ISOMORPHISM BETWEEN SYMMETRIC GROUP ON n SYMBOLS AND THE SET OF ALL n X n PERMUTATION MATRICES.
20:02 THE SET OF ALL n x n PERMUTATION MATRICES FORM A GROUP UNDER MATRIX MULTIPLICATION.
22:25 ORDER OF A PERMUTATION MATRIX IS THE SAME AS THE ORDER OF THE ASSOCIATED PERMUTATION.
23:02 ORDER OF A PERMUTATION MATRIX IN THE GROUP OF ALL PERMUTATION MATRICES.
25:29 WRITING A PERMUTATION AS A PRODUCT OF DISJOINT CYCLES.
26:09 ORDER OF A PERMUTATION IN Sn.
26:46 EXAMPLE OF A PERMUTATION MATRIX OF ORDER 6.
27:00 ORDER OF PERMUTATION MATRIX IS EQUAL TO THE ORDER OF THE ASSOCIATED PERMUTATION.
28:10 DEFINITION OF SIGN OF A PERMUTATION ON n SYMBOLS.
28:25 EXAMPLE: CALCULATION OF SIGN OF A PERMUTATION.
29:45 FORMULA FOR THE DETERMINANT OF A PERMUTATION MATRIX.
30:10 FORMULA FOR THE TRACE OF A PERMUTATION MATRIX.
SORRY ABOUT THE CHANNEL LOGO IN THE MIDDLE OF THE VIDEO. WHEN I WAS STARTING THIS YOUTUBE CHANNEL I DON'T KNOW HOW TO PUT THE LOGO IN A DIFFERENT PLACE. RECENT VIDEOS DOES NOT HAVE THIS ISSUE.
PERMUTATION GROUPS AND PERMUTATION MATRICES,
EVERY DAY I UPLOAD ONE NEW PROBLEM ASKED IN CSIR/GATE/NBHM OR ANY OTHER COMPETITIVE EXAM.
PHD ENTRANCE EXAM SOLUTIONS.
CSIR NET EXAM PREVIOUS YEAR QUESTION SOLUTIONS,
CSIR MATHEMATICAL SCIENCES PREVIOUS YEAR QUESTION SOLUTIONS,
GATE EXAM PREVIOUS YEAR QUESTION SOLUTIONS,
NBHM EXAM PREVIOUS YEAR QUESTION SOLUTIONS.
CSIR NET EXAM JUNE 2021.
CSIR NET EXAM DECEMBER 2021.
IIT JAM 2021. IIT JEE ENTRANCE EXAM. INTERESTING MATHEMATICS PROBLEMS.
PG TRB QUESTION SOLUTIONS.
01:26 PROBLEM STATEMENT.
01:27 DEFINITION OF A PERMUTATION.
01:55 DEFINITION OF A PERMUTATION MATRIX.
03:08 EXAMPLE OF A PERMUTATION MATRIX.
06:43 DIFFICULTIES IN WORKING WITH PERMUTATION MATRICES.
09:46 A BIJECTION BETWEEN PERMUTATIONS IN Sn AND PERMUTATION MATRICES OF ORDER n x n.
10:48 EQUIVALENT DEFINITION OF PERMUTATION MATRICES: EACH ROW AND COLUMN HAS EXACTLY ONE ONE.
11:55 ELEMENTS OF THE SYMMETRIC GROUP ON THREE SYMBOLS S3.
12:18 EXAMPLE: SET OF ALL 3 X 3 PERMUTATION MATRICES.
16:14 EXAMPLE OF A BIJECTION BETWEEN S3 AND THE SET OF ALL 3 X 3 PERMUTATION MATRICES.
17:04 BIJECTION BETWEEN SYMMETRIC GROUP ON n SYMBOLS AND THE SET OF ALL n X n PERMUTATION MATRICES.
17:42 ISOMORPHISM BETWEEN SYMMETRIC GROUP ON n SYMBOLS AND THE SET OF ALL n X n PERMUTATION MATRICES.
20:02 THE SET OF ALL n x n PERMUTATION MATRICES FORM A GROUP UNDER MATRIX MULTIPLICATION.
22:25 ORDER OF A PERMUTATION MATRIX IS THE SAME AS THE ORDER OF THE ASSOCIATED PERMUTATION.
23:02 ORDER OF A PERMUTATION MATRIX IN THE GROUP OF ALL PERMUTATION MATRICES.
25:29 WRITING A PERMUTATION AS A PRODUCT OF DISJOINT CYCLES.
26:09 ORDER OF A PERMUTATION IN Sn.
26:46 EXAMPLE OF A PERMUTATION MATRIX OF ORDER 6.
27:00 ORDER OF PERMUTATION MATRIX IS EQUAL TO THE ORDER OF THE ASSOCIATED PERMUTATION.
28:10 DEFINITION OF SIGN OF A PERMUTATION ON n SYMBOLS.
28:25 EXAMPLE: CALCULATION OF SIGN OF A PERMUTATION.
29:45 FORMULA FOR THE DETERMINANT OF A PERMUTATION MATRIX.
30:10 FORMULA FOR THE TRACE OF A PERMUTATION MATRIX.
SORRY ABOUT THE CHANNEL LOGO IN THE MIDDLE OF THE VIDEO. WHEN I WAS STARTING THIS YOUTUBE CHANNEL I DON'T KNOW HOW TO PUT THE LOGO IN A DIFFERENT PLACE. RECENT VIDEOS DOES NOT HAVE THIS ISSUE.
PERMUTATION GROUPS AND PERMUTATION MATRICES,
EVERY DAY I UPLOAD ONE NEW PROBLEM ASKED IN CSIR/GATE/NBHM OR ANY OTHER COMPETITIVE EXAM.
PHD ENTRANCE EXAM SOLUTIONS.
CSIR NET EXAM PREVIOUS YEAR QUESTION SOLUTIONS,
CSIR MATHEMATICAL SCIENCES PREVIOUS YEAR QUESTION SOLUTIONS,
GATE EXAM PREVIOUS YEAR QUESTION SOLUTIONS,
NBHM EXAM PREVIOUS YEAR QUESTION SOLUTIONS.
CSIR NET EXAM JUNE 2021.
CSIR NET EXAM DECEMBER 2021.
IIT JAM 2021. IIT JEE ENTRANCE EXAM. INTERESTING MATHEMATICS PROBLEMS.
PG TRB QUESTION SOLUTIONS.
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