CSIR PROBLEMS ON DIAGONALIZABLE MATRICES - PART 3

0:00 Intro
0:18 CSIR PROBLEM ON DIAGONALIZABLE MATRICES WITH SOLUTION
2:42 EIGENVALUES OF UPPER/LOWER TRIANGULAR MATRICES ARE ITS DIAGONAL ENTRIES
4:30 DEFINITION OF ALGEBRAIC MULTIPLICITY OF AN EIGENVALUE
5:59 DEFINITION OF GEOMETRIC MULTIPLICITY OF AN EIGENVALUE
6:51 ARITHMETIC MULTIPLICITY GREATER THAN OR EQUAL TO GEOMETRIC MULTIPLICITY
8:20 AM=GM FOR A SIMPLE EIGENVALUE
09:38 A IS DIAGONALIZABLE IF AND ONLY IF GEOMETRIC MULTIPLICITY - GEOMETRIC MULTIPLICITY FOR EACH OF ITS EIGENVALUES
10:05 PROVING A MATRIX IS NON-DIAGONALIZABLE USING ARITHMETIC AND GEOMETRIC MULTIPLICITY
12:51 EXAMPLE OF GEOMETRIC MULTIPLICITY STRICTLY LESS THAN THE ARITHMETIC MULTIPLICITY
13:05 A CSIR PROBLEM ON DIAGONALIZABLE MATRICES WITH SOLUTION
15:13 METHOD TO CALCULATE THE GEOMETRIC MULTIPLICITY OF AN EIGENVALUE
18:38 A REMARK ON JORDAN CANONICAL FORM AND THE DIAGONALIZABILITY OF MATRICES
19:51 EVERY COMPLEX MATRIX IS DIAGONALIZABLE OVER C???
20:01 A CSIR PROBLEM ON DIAGONALIZABLE MATRICES WITH SOLUTION

PART - 1 AND PART - 2 LINK:

AT 8:08 WE ARE SHOWING THAT IF A REAL EIGENVALUE HAS ARITHMETIC MULTIPLICITY ONE THEN ITS GEOMETRIC MULTIPLICITY HAS TO BE ONE. FROM THAT WE CAN DEDUCE THAT IF A REAL MATRIX HAS DISTINCT REAL EIGENVALUES THEN IT IS DIAGONALIZABLE OVER. BECAUSE EACH EIGENVALUE HAS ALGEBRAIC MULTIPLICITY ONE AND HENCE HAS GEOMETRIC MULTIPLICITY ONE. THEREFORE AM=GM FOR ALL EIGENVALUES AND THE MATRIX IS DIAGONALIZABLE.

PROBLEMS ON DIAGONALIZABLE 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.