Discussing the article: "Neural Network in Practice: Pseudoinverse (II)"
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Check out the new article: Neural Network in Practice: Pseudoinverse (II).
Since these articles are educational in nature and are not intended to show the implementation of specific functionality, we will do things a little differently in this article. Instead of showing how to apply factorization to obtain the inverse of a matrix, we will focus on factorization of the pseudoinverse. The reason is that there is no point in showing how to get the general coefficient if we can do it in a special way. Even better, the reader can gain a deeper understanding of why things happen the way they do. So, let's now figure out why hardware is replacing software over time.
In the previous article "Neural Network in Practice: Pseudoinverse (I)", I showed how you can use a function available in the MQL5 library to calculate the pseudoinverse. However, the method present in the MQL5 library, as in many other programming languages, is intended to calculate the pseudoinverse when using matrices or at least some structure that may resemble a matrix.
Although this article shows how to perform multiplication of two matrices, and even factorization to get the determinant of any matrix (which is important to know whether a matrix can be inverted or not), we still have to implement one more factorization. This is necessary so that you can understand how factorization is performed to obtain pseudoinverse values. This factorization consists of generating the inverse matrix.
But what about transposition? Well, in the previous article, I showed how to perform a factorization that simulates the multiplication of a matrix by its transpose. So, executing such an operation is not an issue.
Author: Daniel Jose