Hello guys, Welcome to Africa's Largest Video Search Engine, and you are watching The Gram Schmidt Orthogonalisation Process: A Mathematical Explanation.. and this video is uploaded by Ganesh Institute at 2019-06-04T10:32:19-07:00. We are just promoting this video only for entertainment and educational purpose only. I hop you like our Video Search Engine. [fdsgsMP9JnA]
| Name | The Gram Schmidt Orthogonalisation Process: A Mathematical Explanation. |
| Video Uploader | Video From Ganesh Institute |
| Upload Date | This Video Uploaded At 04-06-2019 17:32:19 |
| Video Discription | Gram Schmidt Orthogonalisation Process is one of the most popular techniques for linear algebra. It is an optimization algorithm for solving the least squares problem in linear regression. The idea behind Gram Schmidt Orthogonalisation Process is to find a set of orthogonal matrices that would be able to produce a better fit to an assumed model than the current set of matrices. The Gram Schmidt Orthogonalisation Process can be used in many different fields, including economics, physics, and engineering. If you are interested in learning more about this process, keep reading! The Gram Schmidt Orthogonalisation Process: A Mathematical Explanation. Gram Schmidt Orthogonalisation Process is one of the most popular techniques for linear algebra. It is an optimization algorithm for solving the least squares problem in linear regression. The idea behind Gram Schmidt Orthogonalisation Process is to find a set of orthogonal matrices that would be able to produce a better fit to an assumed model than the current set of matrices. The Gram Schmidt Orthogonalisation Process can be used in many different fields, including economics, physics, and engineering. If you are interested in learning more about this process, keep reading! What is Gram Schmidt Orthogonalisation Process? The Gram Schmidt Orthogonalisation Process is a procedure for linear algebra. This process will find the best set of orthogonal matrices that would be able to produce a better fit to an assumed model than the current set of matrices. This process originated in 1843, when Danish mathematician Rasmus Bartholin devised it as one way to solve the least squares problem in linear regression. The problem with this technique was that there were many ways to compute the least squares solution, but none of them were known to be better than others. The Gram Schmidt Orthogonalisation Process was conceived as an algorithm that would choose the best possible solution for this problem. It helps find the right matrix by inspecting all possible solutions and picking out the ones with the highest residual variance. When you want to use this process, you need to make sure you have an initial set of orthogonal matrices which are used as a starting point. You can then calculate new orthogonal matrices using Gram-Schmidt's algorithm until you reach convergence, which is when your change in residual variance drops below some threshold value after each iteration. How does Gram Schmidt Orthogonalisation Process work? The Gram Schmidt Orthogonalisation Process is a linear algebra algorithm and it can be used in many different fields. The process is used when there are two sets of equations and one set of unknowns. The goal is to find a set of orthogonal matrices that would be able to produce a better fit to the assumed model than the current set of matrices. The first step involves picking an initial matrix, which is the basis for the solution. Next, all columns of this matrix are multiplied by a new, orthogonal matrix that has been generated from the previous column where each entry was replaced with its complex conjugate. For example, if we had: A = (1 2 -1) We could rewrite this as: A' = (1-2i 1+2i) Following these steps will lead us to our final result: A'' = (1-4i 2+4i 0 0). The applications of Gram Schmidt Orthogonalisation Process As stated before, the Gram Schmidt Orthogonalisation Process can be used in many different fields, including economics, physics, and engineering. One of the most popular examples of this process is linear regression. The Gram Schmidt Orthogonalisation Process is often used in linear regression to find a set of orthogonal matrices that would be able to produce a better fit to an assumed model than the current set of matrices. There are many other applications for this process that do not need to be related to linear algebra. For example, if you wanted to implement an efficient algorithm for finding the shortest path between two nodes on graph with non-uniform costs, you could use Gram Schmidt Orthogonalisation Process. Conclusion Gram Schmidt Orthogonalisation Process is an algorithm to make orthogonal matrices. It is widely used in mathematics, engineering, and statistics. [fdsgsMP9JnA] |
| Category | Education |
| Tags | #education | ignou | basis | btech |
