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 Aug 29 awarded Notable Question Sep 17 awarded Popular Question Jul 31 awarded Nice Answer Sep 5 asked Which subject deals with questions like “Distance from hyperplane to a point” Sep 4 comment Applications/Motivations of matrix decomposition techniques Are you saying that the purpose of SVD is to approximate? Sep 4 comment Applications/Motivations of matrix decomposition techniques Well, I am still confused. Is everyone implying here that Matrix decomposition techniques were primarily invented to overcome computational limitations. In that sense it is more of an strategy to improve the speed or accuracy of other real algorithms. I was under the assumption that Matrix decomposition also provides additional insights into the properties of the matrix in itself; In way I was hoping for Matrix decomposition to be more of a tool for a Mathematician deriving proofs rather than to an engineer who needs to implement a particular numeric algorithm Sep 4 asked Applications/Motivations of matrix decomposition techniques Sep 4 comment How to calculate gradient of $x^TAx$ What is $M_{n}(ℝ)$ .. Manifold? Sep 3 revised How to calculate gradient of $x^TAx$ added 4 characters in body Sep 3 awarded Scholar Sep 3 accepted How to calculate gradient of $x^TAx$ Sep 3 comment How to calculate gradient of $x^TAx$ Yes! Thanks a lot! Sep 3 awarded Student Sep 3 awarded Supporter Sep 3 comment How to calculate gradient of $x^TAx$ The above comments by others indicate that he applied the product rule for differentials. Unfortunately, I am unable to find a proof for the result of product rule for differentials. Any help there would be great. Sep 3 comment How to calculate gradient of $x^TAx$ The lecture says that using the properties of external definition of derivative, we can avoid representing it as "sums" and this simplifies the whole calculation Sep 3 comment How to calculate gradient of $x^TAx$ Thanks. It's product rule indeed. But, where can I find a proof for the product rule for multivariable functions using differentials? I am not finding en.wikipedia.org/wiki/Product_rule convincing because uses the term differential very loosely. Is there a product rule proof using differential form properties? Sep 3 asked How to calculate gradient of $x^TAx$ Sep 2 awarded Editor Sep 2 revised How to prove matrix differential rules using differential forms rules added 178 characters in body