coursera linear algebra

) 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

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Prepare to write an article about Singular Value DecompositionArticleIt suddenly found that it needed a lot of linear algebra knowledge. Therefore, we will first introduce the basic concepts and operations of linear algebra to help readers understand Singular Value Decomposition. 1. Basic Concepts A matrix is a numbe

A very important concept in linear algebra is the vector space r^n, which will focus on a series of properties of vector space.A vector space is a non-empty set v consisting of some vector elements, which needs to satisfy the following axioms:The subspace H of the vector space V needs to meet the following three conditions:The two theorems are in the elaboration of how to form subspace, and its proof simply

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

transformed in order to find a suitable linear combination(linear combination) that makes AX = bThe corresponding diagramVector b is a sum of two col vectorsHere again, when Vector x is taken, we can get the entire XY plane, meaning that whatever vector B can find the corresponding solution(not when two col vectors are parallel)* The practice of column picture does not seem to be emphasized in schools, but

Matrix equation:We have previously introduced the linear combination of vectors, the form of X1a1+x2a2+xnan, that we can use to express them with [] formulas. (This expression is sought for convenience and unity of computation), and we give the following definition to give another form of the linear combination of vectors.It can be seen that the right side of the equation, the form of a vector combination,

be extracted by an array named key;The Savetxt (), Loadtxt () function can read and write a text file that holds a one-dimensional and two-dimensional array, outputs the text separated by the spacer, specifies the spacer by the delimiter parameter, and the default output is in the form of '%.18e ', separated by a space by default.4. Memory-mapped arraysCreates a memory-mapped array from a file that reads the specified offset data,> without reading the entire file into memory by Memmap ():FileNa

assume that the line expression is as follows:Then calculate the error function:The error function e is obtained by the deviation of the coefficient, a, a, and the 0:The value of the coefficients, a, a, a, and a linear expression is obtained by the above formula:The curves obtained by the least squares are as follows:Linear algebraic approach to least squares: Similarly, the expression of a fitted line is set to:The purpose of fitting is to make the

Least squares problem:Before the combination of orthogonal, subspace W, orthogonal projection, orthogonal decomposition theorem and best approximation principle in vector space, the least squares problem can be solved satisfactorily.First of all, we have to explain the problem itself, that is, in the process of production, for the giant linear systems ax=b, may be no solution, but we are urgently need a solution, satisfies the solution is the most app

1. Determinant1.1 Second-order determinant1.2 third-order determinant1.3 Number of reverse order1.4 N-Step determinant2. The nature of the determinantProperty 1 The determinant is equal to its transpose determinant.Property 2 swaps the determinant of two rows (columns), determinant.Property 3 The determinant of a row (column) in which all elements are multiplied by the same multiplier K, equals the number k multiplied by this determinant.Property 4 Determinant If there are two rows (column) elem

This chapter begins with an introduction to another basic concept in linear algebra-the determinant.In fact, like the Matrix, the determinant is also a tool for simplifying the expression polynomial, about the historical origin of the determinant, as the following introduction.In introducing the inverse matrix, we have mentioned that the second-order matrix has a corresponding determinant based on matrix A

algebra review, I'll be the using one index vectors. Most vector subscripts in the course start from 1.When talking on machine learning applications, sometimes explicitly say if we need to switch to, when we need to use The zero index vectors as well. Discussion of machine learning applications will be converted to subscript starting from 0.Finally, by Convention,use upper case to refer to matrices. So we ' re going-letters like a, B, c.and usually w

Mymathlib and the computing experience.PNS) Ab=e, then a A, a, a and a inverse of the inverse of the a,a is equal to the determinant value of the inverse of the determinant is worth reciprocal; The inverse of the inverse B of the product of AB multiplied by the inverse of A; A reversible, a transpose inverse equals inversion of the transpose;38) Special matrix: All matrices, quantity matrix, diagonal matrix, quasi-diagonal matrix, upper triangular matrix, lower triangular matrix, symmetric matr

Reference: Hiraoka and luckily Programmer's Math 3: linear algebra. 1. Vector-- What is the space 1.1 vector? Vectors, which can be seen as a pile of permutations.In space, a vector can represent a point, for example (2,3) that represents a point with a horizontal axis of 2 on a two-dimensional plane, an ordinate of 3, or a directed segment that points to it from the origin.When emphasizing the concept of "

In this chapter we discuss the relationship between the vectors defined in the R^n space, which is generally orthogonal, then the orthogonal projection, the best approximation theorem, and so on, these concepts will lay the foundation for the optimal approximate solution of the ax=b of linear equations with no solution.Orthogonality:To give the simplest example, in a plane, if the two-dimensional vector's point multiplication is 0, then we can determi

3 31 2 4 % % The basis of zero space: the Code of this zero space is worth looking at, reflecting the basic idea of column meaning in linear algebra. You may not know what the code is. A simple statement may contain many operations. I like to give an example when I don't quite understand it. Let's take a look at the code in one sentence. Note that The column in the zero space indicates the

transformation.Matrix elimination Element Method:determinant TypeCalculation (0 descending order method)Other properties of the determinant:The law of ClydeMatrixFollow the law1. Linear Properties2. Operational and polynomial of n-order matricesElementary matrix and its role in multiplicationFor the unit matrix, the matrix obtained by making an elementary transformation becomes the elementary matrix.Together there are three primary transformations:Th