Transcript:

[MUSIC] LM high package provides basic functions for manipulating large arrays and matrices of numerical data. The Syfy package extend their functionality of numpy to be specific. SIFY is a library that used numpy for more mathematical functions. Syfy’s used numpy surace as the basic data structure and comes with modules for various commonly used it tasks such as linear algebra, integration, ordinary differential equations and signal processing. In this video we reduce. IP linear algebra modules to show you some commonly used linear algebra functions. Ursaring first. We need to import numpy and also we need to import the linear algebra from SIFY module. So let me show you how to solve a linear system by using the solve function, So let’s say, for example, we have umpire Ray. You that we have from three, two and one minus one. This is the equation, and then we have. The first equation is the equals to 2 and the second equation is equal to 4 and then side B. And then we can use the linear algebra function, which is hold it. Doc, solve so the ace linear equation. So here is the cells here because we have to equation and to unknown, so we have a perfect solutions, sometimes we. Mike’s come Mikasa SIS. Linear system that have unbalanced that a long N equation. So let’s say, for example, we have a look at the five you eight. And then in that case, the talks all functions cannot help you to solve their problems because the input them needs to be a square matrix here in order to for us to solve this problem. We need to use the least square approximation so here we can simply change it to change the solve to E square and see is the result. Now you can see. This is the optimal result when we have the unbalanced and equation and unknown. So right here, we have the three equations and two unknowns and the result is best fits. So on the other hand, we can actually have more unknown than the equations and linear algebra functions right here can also help you to solve the problems by using the East gray approximation apart from solving the linear system, we can also use the–some linear algebra functions modules to solve some to compute some inverse determinants on the P inverse. Let’s say, for example, it would like to of thee. Inverse of these a/e just changes to a epital a which means matrix and we can also computer determinants of this A and when the matrix is not a square matrix, we can also use the. P inverse to impurity generalize, the inverse, the linear algebra modules also provide functions to calculate long. So change it to it. Better show you to Calculon doll here, so say, for example, we calculate the too long, which provide you the ordinary distance from their origins to the point. Three four right here. So five is the result, and then we can also calculate the error one norm, which value the longest distance travel from their origin to the pawn of before right here and we can also calculate the arrow infinity. Lom, so I providing the numpy infinity. So which give you the largest mela tube within the each of the wetter and under this wetter for is the largest rally in this linear algebra modules, we can also perform matrix decomposition say, for example, on to freeform matrix and unto. Oh, compose these matrix. So we have Lambda. I can be the eigen value and also the eigenvector you. So this Lambda is the eigen value. Mv Steve. I can better you. Here’s the I pull. So these other eigenvalue and these are the eigen vector. We can also apply a singular value decomposition here when we have a non-square matrix say, for example, we have East own square matrix, and then we want to use the Tsing singular value decomposition here. The function is as we so the you ear is the left singular vector and VH is the right singular better. So this small capital letter S is just an array of the singular value, so in order for you to calculate to have the singular matrix, we need to use the in other functions. Is the near algebra here. Diagonal a sweetie. Here we input the shape of the of the original matrix of original matrix before the singular value decomposition, and then we just put in the diagonal matrix for T cell but is singular or singular matrix. So let me show you a singular matrix. So the singular value array has been put inside this singular matrix. You can use their top product to get better results for a But I’m not going to show here and that’s it. I hope you have a better understanding of the linear algebra modules inside Pi. Thank you for watching.