https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transpose-of-a-matrix 2021-04-12T12:34:15Z Transpose of a matrix Transpose of a matrix Sal Khan video https://cdn.kastatic.org/googleusercontent/K-eylR9ausKgxbpubZJ3jsdmAcC86f54EiATVv89S-Ldc78nDCgZEBvKDZwbKwPn4iZlMbgr97PoXuNFQM7HLcM Transpose of a matrix Transpose of a matrix https://cdn.kastatic.org/ka-youtube-converted/2t0003_sxtU.mp4/2t0003_sxtU.mp4 517 Transpose of a matrix https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transpose-of-a-matrix-product 2021-04-12T12:34:15Z Transpose of a matrix product Taking the transpose of the product of two matrices Sal Khan video https://cdn.kastatic.org/googleusercontent/7cgi6vPxXZW4y0hOzfm2Yu8Wy5Fsx7xTwB219fVEtmM-RX3GHruNuVauvziurkm2oOZmgoj8PkohkyEljlEMwn2g8A Transpose of a matrix product Taking the transpose of the product of two matrices https://cdn.kastatic.org/ka-youtube-converted/UdHgWK13x5I.mp4/UdHgWK13x5I.mp4 530 Transpose of a matrix https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transposes-of-sums-and-inverses 2021-04-30T23:54:23Z Transposes of sums and inverses Transposes of sums and inverses Sal Khan video https://cdn.kastatic.org/googleusercontent/etemSjrsjp51AvPUaQoKQDNLqyEgUuDptnM-FdczQuK6tCvVZQoxs5ahfxpddeXYv49yDNMlomiSTfw89aWYJB_p Transposes of sums and inverses Transposes of sums and inverses https://cdn.kastatic.org/ka-youtube-converted/Br_8t58mdeI.mp4/Br_8t58mdeI.mp4 521 Transpose of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/properties-of-transpose-of-the-matrices 2025-05-22T13:12:03.767544849Z Properties of transpose of the matrices In this video, we learn about the properties of a transpose of a matrix. We first look at the properties and then dive deeper to understand how they work. We look at these properties - Transpose of a transpose, Multiplying with a scalar, Transpose of a sum, and Transpose of a product. We finally solve a practice problem to test our knowledge. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Properties of transpose of the matrices In this video, we learn about the properties of a transpose of a matrix. We first look at the properties and then dive deeper to understand how they work. We look at these properties - Transpose of a transpose, Multiplying with a scalar, Transpose of a sum, and Transpose of a product. We finally solve a practice problem to test our knowledge. https://cdn.kastatic.org/ka-youtube-converted/Yaqaz-PO6TI.mp4/Yaqaz-PO6TI.mp4 579 Transpose of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/e/properties-of-matrix-transposes 2026-04-14T11:30:38.220334671Z Properties of matrix transposes Properties of matrix transposes Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:transpose-of-matrix/v/symmetric-and-skew-symmetric-matrices 2025-05-22T13:12:03.767544849Z Symmetric and skew symmetric matrices In this video, we talk about symmetric and skew symmetric matrices. We first look at examples of each and then understand the constraints on the elements. We then verify 2 results that work for sum and difference of a matrix and its transpose. We finally derive these results using properties of transpose of a matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Symmetric and skew symmetric matrices In this video, we talk about symmetric and skew symmetric matrices. We first look at examples of each and then understand the constraints on the elements. We then verify 2 results that work for sum and difference of a matrix and its transpose. We finally derive these results using properties of transpose of a matrix. https://cdn.kastatic.org/ka-youtube-converted/5zIK-D1DVgo.mp4/5zIK-D1DVgo.mp4 468 Transpose of a matrix https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:matrices-ncert-new/x6f66cbee9a2f805b:transpose-of-matrix/e/symmetric-and-skew-symmetric-matrices 2026-04-14T11:30:38.220334671Z Symmetric and skew symmetric matrices Symmetric and skew symmetric matrices Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/expressing-as-a-sum-of-symmetric-and-skew-symmetric-matrix 2025-05-22T13:12:03.767544849Z Expressing as a sum of symmetric and skew symmetric matrix In this video, we leverage the results derived in the previous video to express any given matrix as a sum of a symmetric and a skew symmetric matrix. We first review these results. We add half of sum to half of difference to get the desired outcome. We finally practice a problem we express a 3x3 matrix as a sum of a symmetric and a skew symmetric matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Expressing as a sum of symmetric and skew symmetric matrix In this video, we leverage the results derived in the previous video to express any given matrix as a sum of a symmetric and a skew symmetric matrix. We first review these results. We add half of sum to half of difference to get the desired outcome. We finally practice a problem we express a 3x3 matrix as a sum of a symmetric and a skew symmetric matrix. https://cdn.kastatic.org/ka-youtube-converted/MGJTiljFtiw.mp4/MGJTiljFtiw.mp4 394 Transpose of a matrix https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/e/expressing-as-a-sum-of-symmetric-and-skew-symmetric-matrix 2025-08-08T02:45:51.78671331Z Expressing as a sum of symmetric and skew symmetric matrix Expressing as a sum of symmetric and skew symmetric matrix Ashish Gupta exercise