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Tutorial 7: Transpose of matrices and Its properties
- 1. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Basic Mathematics: Transpose of matrices and Its properties Dr. Mehar Chand Department of Mathematics Baba Farid College, Bathinda-151001 April 28, 2020 Dr. Mehar Chand Transpose of matrices
- 2. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Contents 1 Transpose of matrices 2 Properties 3 Symmetric Matrix 4 Skew-Symmetric Matrix 5 Theorems 6 Some Examples 7 Full video Lecture Dr. Mehar Chand Transpose of matrices
- 3. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Transpose of matrices Definition (Transpose of matrices) Let A be any matrix. The Matrix obtained by interchanging rows and columns of A is called transpose of A and is denoted by A or At or AT Thus if A = [aij ]m×n, then A = [aji ]n×m Dr. Mehar Chand Transpose of matrices
- 4. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Properties of Transpose of Matrices Property 1 (A ) = A, for any matrix A 2 (A + B) = A + B , where A and B are matrices of same order 3 (AB) = B A provided AB is defined 4 (kA) = kA , where A is any matrix and k a scalar Dr. Mehar Chand Transpose of matrices
- 5. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Symmetric Matrix Definition (Symmetric Matrix) A square matrix A is said to symmetric if A = A Dr. Mehar Chand Transpose of matrices
- 6. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Skew-Symmetric Matrix Definition (Skew-Symmetric Matrix) A square matrix A is said to skew-symmetric if A = −A Dr. Mehar Chand Transpose of matrices
- 7. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Theorems on Transpose of Matrices Theorem (1) For any square matrix A, A + A is symmetric and A − A is skew-symmetric matrix Theorem (2) Every square matrix can be uniquely expressed as sum of symmetric and skew-symmetric matrix Theorem (3) All diagonal entries of skew-symmetric matrix are zero. Dr. Mehar Chand Transpose of matrices
- 8. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Examples See the full lecture for the examples, the link of video lec- ture is given in the next slide. Dr. Mehar Chand Transpose of matrices
- 9. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Full video Lecture To see full video lecture visit the below link http://drmeharchand.com/basic-mathematics/ Dr. Mehar Chand Transpose of matrices
- 10. Transpose of matrices Dr. Mehar Chand Transpose Properties Symmetric Matrix Skew- Symmetric Matrix Theorems Some Examples Video Thank you Dr. Mehar Chand Transpose of matrices