Hello everybody. Welcome to our lecture, Introduction to Linear Algebra Functions in Python. There are many function in Python and many of them are used in linear algebra. In this lecture, I'm going to discuss some of the most useful function in linear algebra. First, we need to import numpy and we need to build our matrices. Let's say matrices M, N and O. We're going to build those. Then as well as three vectors so that v1, v2, and v3. Now the first function that I want to discuss is the dot function. The dot function will return with products of two metrics or two vectors. If the inputs are matrix, so it will return to the product of those two metrics. If input are vectors, then it will return the product of those two vectors. Next, the multidot. This should be multidot. This function will take several matrices and then it will return the product of those matrices. You see I've got three matrices, M, N, and O. If you insert this into the usual dot, you will get an error message. If you're taking the product of more than two matrices, it is a good idea to use multidot method. In addition to multidot method, there is another method called vdot. This vdot return the product of two vectors. It does not perform matrix multiplication well. It will return a wrong answer. This method should be used for vectors only. Let's say I want to find vdot the vector product of v1 and v2. Then I will say np.vdot v1, v2. Get that. The inner product will return the inner product of two rays in other words the inner product of two vectors. For example, if I have vector v2, v3, and v1, the inner product is equal this. Multimultiplications. It's time for matrix multiplication function. This will return the product of two matrix but it does not take more than two. That's the difference between this and multidot. This would return the product of matrix M and N. So linalg.matrixs_power M, n. It will raise the matrix M to the power n. For example, if I have a matrix M, 3, it will raise this matrix M to the power of three. Then this is the result where the matrix M is raised to the power of three. Linalg.eig, stand for eigenvalue and eigenvector. Then on that E-I-E-G O all will return the eigenvalues and eigenvectors of the matrix O. If I set eig_vals be the eigenvalues of this matrix O and eig_vects to be the eigenvectors of this matrix O, then we can prime each one of them one by one. So eig_vals. We can do the same thing with eig_vects. We had three vectors. We should get three vectors. These are the three vectors. This is the first one and the second one, that's a j, then the third one, i, j, k. Each vector has got three component. First one, second one is here, and the third one is here. In addition to that, we also have an linalg.eigh. This will return the eigenvalue of complex Hermitian matrixs. If your matrixs is complex for example, or if you have a real symmetric matrix for example, our matrix and real symmetry is a four by four, is a square matrix. This method will return it. Even if you have a measured hermitian complex number in it, we will return the eigenvalues first and then eigenvectors next. Also that's the difference between this and linalg.eigh. Eigh will deal with complex even if you have complex numbers. Now linalg.det, this det stands for determinant of matrixs N. We determine the metrics N. It is the metrics N here is the core negative 2.00. Then linalg.n will open the inverse of the matrix M. The inverse exists because the determiner is different from 0 here. Thanks everybody. I will see you in the next lecture where we're going to do more metrics operations. In this lecture we'll learn how to discuss different functions of different linear algebra function in Python and then now do an example of each one of them. This is not all of them. The list is not exhaustive, but these are the most popular. Thanks everybody. See you next time.
