This week has focused on a number of topics, including:1) from the perceptual knowledge of what is linear algebra, and from the ideological realization that linear algebra is useful.2) Simple understanding of the addition, subtraction, multiplication of the matrix. These are some of the rules that people prescribe. Mas
This article is a basic learning blog from the University of Paris, PhD Hadrien Jean, which aims to help beginners/Advanced Beginners Master the concept of linear algebra based on deep learning and machine learning. Mastering these skills can improve your ability to understand and apply a variety of data science algorithms.For beginners, the theoretical underpinnings of deep learning (Ian Goodfellow, Yoshua
, single non-zero vector linearly independent;27) The sufficient and necessary condition for the linear correlation of a vector group is that one of the vectors can be linearly represented by the remaining vectors;28) The sufficient and necessary condition for the linear correlation of two vectors is that their components correspond proportionally;29) The vector group is linearly correlated with the partial
PCA Dimension Reduction-- Minimum Variance interpretation (linear algebra see PCA) Note: According to the online data collation, welcome to discussThe complexity of the machine learning algorithm is closely related to the dimensionality of the data, even with the dimension number of the exponential association. So we have to dimensionality the data.dimensionality, of course, means the loss of information,
Chapter 2 determining factors
§ 1 Introduction
Solving equations is a basic problem in algebra. Especially in the algebra learned by Middle School, solving equations plays an important role. This chapter and the next chapter mainly discuss the General Multivariate equations, that is, linear equations.
The theory of linear
the linear Equation Group general solution, This allows us to directly transform the vector equation into an augmented matrix to solve the problem.Meaning of the span symbol: based on a linear combination of concepts, we remember that span (V1,v2,v3,..., vn) represents a collection of all linear combinations of v1~vn of these n vectors.Based on this concept of t
The first self-taught Tongji 5 version of the linear algebra, from the beginning to look, also a little puzzled, suddenly there are many determinant appear, in fact, the definition of the real does not understand.Refer to the Li Shangzhi teacher's linear Algebra 2 video and make some notes to enhance understanding.1. T
has another well-structured similarity matrix, which makes the elementary transformation very convenient. It makes a discussion of the similarity matrix of the \ (a\), which is equivalent to the discussion of the similarity matrix of the \ (b=\begin{bmatrix}\lambda_0\\\bar{\lambda}_0\end{bmatrix}\).\[\begin{bmatrix}1\\\lambda^{-1}\\\ddots\\\lambda^ {-(n-1)}\end{bmatrix}\begin{bmatrix}\lambda1\\\ddots\ddots\\\ddots 1\\\lambda\end{bmatrix}\begin{bmatrix}1\\\lambda\\ \ddots\\\lambda^{(n-1)}\end{bm
BlasThe BLAS (Basic Linear Algebra subprograms) is routines, provide standard building blocks for performing Basic vector and matrix operations. The level 1 BLAS perform scalar, vector and vector-vector operations, the Level 2 BLAS perform matrix-vector operations, a nd the Level 3 BLAS perform matrix-matrix operations. Because the BLAS is efficient, portable, and widely available, they is commonly used in
Chapter 1 introduce to VectorsTwo core operations of linear algebra: vector addition and multiplication. Combining these two operations is a linear combination of vectors.1.1 Vector and Linear combinationsTwo basic operations: vector addition and multiplication.two x vector v and W
Make a mark and have time to summarize the knowledge of the linear algebra obtained in the 10-day course to finish a book.1. Determinant: The value can be evaluated2, Matrix: There is a corresponding determinant, the matrix itself can not calculate a value, but can be by the equivalent determinant of the value of the matrix and the adjoint matrix, whether reversible, is also a
Mastering linear algebra in 10 days: astoundin
Translator: mapleflying
Recently, my friend Scott Young made an amazing feat: within a year, he completed all 33 of the legendary mit computer science curriculum, from Linear Algebra to Computational Theory. The most important thing is that he is self-taught. He watches
This paper turns from the public number---meets the mathematical---graphic mathematical---linear algebra partThank you for meeting the Math Working Group to explain the obscure and acting knowledgeable mathematical knowledge of university textbooks in an easy-to-understand and lively and interesting way.The concept of vectorsIn real life, we put a few values together, as a whole to analyze, and this has vec
Directory
Linear Algebra
I. Basic Knowledge
Ii. vector operations
Iii. Matrix Operations
Linear Algebra 1. Basic Knowledge
All vectors in this book are in the form of column vectors:\ [\ Mathbf {\ VEC x} = (x_1, x_2, \ cdots, X_n) ^ t = \ begin {bmatrix} X_1 \ X_2 \ vdots \ x_n \ end {bmatrix} \] all
The previous articles on linear algebra are all explained in terms of mathematics. This article will be a different angle to explain the problem.The tutor often tells me that everything has to think about its physical or practical significance, through the phenomenon to see the essence, so that can be more profound understanding, so you can see what the actual use of li
) Elementary factor:?? Use?? The elementary transformation of the lambda matrix will be a characteristic matrix?? The λe-a is transformed into a diagonal matrix, and then each diagonal element is decomposed into the product of a non-identical one-power-exponent, then all of these power-of-one-powers are referred to as the elementary factors of A;The sufficient and necessary condition for the similarity of N-order matrices A and B is that their elementary factors are the same;20) about when the m
This paper turns from the public number---meets the mathematical---graphic mathematical---linear algebra partThank you for meeting the Math Working Group to explain the obscure and acting knowledgeable mathematical knowledge of university textbooks in an easy-to-understand and lively and interesting way.This time we mainly do a review, and then further the determinant of the geometric meaning of the animati
Mastering linear algebra in 10 days: astoundin
Translator: mapleflying
Recently, my friend Scott Young made an amazing feat: within a year, he completed all 33 of the legendary mit computer science curriculum, from Linear Algebra to Computational Theory. The most important thing is that he is self-taught. He watches
of the lectures Started by this teacher are very good, because our linear algebra textbooks are similar. They all start from the determinant, followed by the matrix followed by the vector, I didn't quite understand the arrangement of books before, but now I am wearing it all at once:
Linear Algebra is used as a too
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