Category: Mathematics

2.3 Elimination Using Matrix 2

2.3 Elimination Using Matrix

The main purpose of linear algebra is to solve linear equations, we have learned the systematic method, elimination, last post. Today, We are trying to do elimination through matrix. The goal is to express all the steps of elimination (and final result) in a more clear way. And we will develop an important operation — Matrix Multiplication.

1.1 Sample sets 0

1.1 Sample sets

Today we begin our new category of blogs, and they are about probability theory. To begin with, I have to say that the knownledge in these blogs are elementary, while, that just means they are simple and basic but not unimportant. However, these concepts in the following blogs are foundations of the whole probability theory.
The first bolg contains basic concepts of “Set Theory”, and the probability theory is built on them.

2.2 The Idea of Elimination 0

2.2 The Idea of Elimination

We have talked about that the central problem of linear algebra is to solve linear equations. A systematic way to solve linear equations are “Elimination”. And in this post we will inspect “Elimination”.

2.1 Vectors and Linear Equations 0

2.1 Vectors and Linear Equations

Last chapter we have learned something about linear algebra — vectors, linear combinations and something else. Although they are easy´╝îthey are the crucial concepts of linear algebra. This post we are going to talk about how to solve a system of equations. And I have to say, this is the central problem of linear algebra.

1.3 Introduction to Matrices 0

1.3 Introduction to Matrices

Vectors are the element of linear algebra, and we can consider vectors and their linear combination as the roots of linear algebra. However, if we solved all the problem with vectors, the progress would become cumbersome, so we need something more deft, and now let me present **matrix**, who is the most used object in linear algebra. And in this post another concepts, independence and dependence, about vector will be described.

1.2 Lengths and Dot Products 0

1.2 Lengths and Dot Products

After linear combination, today we are going to meet another simple but important concept — Dot Products. And dot products can produce some other interesting concepts or so.

1.1 Vectors and Linear Combination 0

1.1 Vectors and Linear Combination

This post series is an introduction to linear algebra. It’s simple and even naive, However, the important position of linear algebra won’t be changed. In artificial intelligence and other subjecs of engineering, linear algebra is the one of the most important foundation. So we need to review it again and agian, and it won’t waist our time at all, but, on the contrary, we can save a lot of time in our futher research. And Linear algebra theories can help us come up with some new ideas in our field.