
Title: Introduction

Series: Linear Algebra

YouTubeTitle: Linear Algebra 1  Introduction

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Quiz: Test your knowledge

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Timestamps
00:00 Introduction 00:50 Linear Algebra applications 02:20 Visit to the abstract level 03:00 Concrete level 03:40 Prerequisites 04:10 Credits 
Subtitle in English
1 00:00:00,880 –> 00:00:06,560 Hello and welcome to linear algebra A whole video course I designed for everyone
2 00:00:06,560 –> 00:00:12,160 who wants to start with the basics in mathematics and in the end wants to master vectors,
3 00:00:12,160 –> 00:00:17,760 vector spaces, matrices and so on. However, before we start I really
4 00:00:17,760 –> 00:00:21,280 want to thank the nice supporters that make this course possible.
5 00:00:22,080 –> 00:00:26,480 Each small contribution on Steady or PayPal makes it easier for me to spend
6 00:00:26,480 –> 00:00:28,400 to create these videos here.
7 00:00:29,360 –> 00:00:34,480 Therefore, on Steady you find quizzes and the pdf versions for all the videos here.
8 00:00:35,520 –> 00:00:41,840 Okay, now you might know I already have some calculation videos in linear algebra.
9 00:00:41,840 –> 00:00:45,680 But with this course here, you finally get the whole structure
10 00:00:45,680 –> 00:00:50,480 and should be able to learn linear algebra, by watching the videos in the right order.
11 00:00:51,440 –> 00:00:56,640 Indeed, linear algebra as a whole is a very important topic in mathematics,
12 00:00:56,640 –> 00:00:58,880 and it has a lot of different applications.
13 00:01:00,080 –> 00:01:04,400 One application, I can visualise immediately with a short drawing here.
14 00:01:05,360 –> 00:01:10,000 Just imagine in the problem you want to solve, a lot of variables are involved.
15 00:01:10,880 –> 00:01:14,720 For example, we could have some fixed quantities, we just call
16 00:01:14,720 –> 00:01:18,160 a, b, c, d and so on. And on the other hand,
17 00:01:18,160 –> 00:01:21,920 we also could have some variables where we don’t know the value yet.
18 00:01:22,960 –> 00:01:26,720 Therefore, we call them unknowns, and here we denote them by x,y,z.
19 00:01:28,640 –> 00:01:33,440 Hence, in order to solve your problem. You want to find possible values for x,y,z.
20 00:01:35,040 –> 00:01:40,880 And exactly there, linear algebra can help when we know the relations between the quantities.
21 00:01:41,760 –> 00:01:47,440 However, it turns out, we need simply relations between our variables.
22 00:01:48,640 –> 00:01:55,360 Then, when we have this, we can use linear algebra to find all possible solutions for the unknowns
23 00:01:56,560 –> 00:02:02,240 Therefore, linear algebra is the important tool which helps us solving our problem.
24 00:02:03,200 –> 00:02:04,320 So, you could say:
25 00:02:04,320 –> 00:02:09,040 Giving calculation rules for solutions is one part of linear algebra.
26 00:02:10,160 –> 00:02:16,000 Indeed, this is important. But in order to understand the topic in a whole,
27 00:02:16,000 –> 00:02:21,120 we need to go abstract. Therefore, this abstract level is something,
28 00:02:21,120 –> 00:02:26,560 we also will discuss in this course. For example, on this abstract level,
29 00:02:26,560 –> 00:02:30,160 we will find a fundamental concept we call a vector space.
30 00:02:31,200 –> 00:02:35,840 Then, in this space, we will find objects, we call vectors.
31 00:02:36,480 –> 00:02:40,480 And we will find out, we can do a lot with these vectors,
32 00:02:40,480 –> 00:02:44,160 which leads us to a new concept, we call a linear map.
33 00:02:45,280 –> 00:02:49,840 Hence, there we have now something that can transform vectors.
34 00:02:50,720 –> 00:02:55,520 Now, please don’t be deterred here because we don’t start at the abstract level.
35 00:02:56,400 –> 00:02:59,120 First, we will consider we will consider a very concrete level.
36 00:03:00,080 –> 00:03:06,000 This means, instead of an abstract vector space, we start with something, we can call Rn.
37 00:03:07,440 –> 00:03:10,720 Then, on this level, a linear map just corresponds to
38 00:03:10,720 –> 00:03:16,320 something we can put into a table. And such a table, we just call a matrix.
39 00:03:17,200 –> 00:03:19,440 Okay, now we now: In this course,
40 00:03:19,440 –> 00:03:24,640 we first discuss the concrete level here and then we go to the abstract level afterwards.
41 00:03:25,680 –> 00:03:28,640 Of course, there are some prerequisites for this course
42 00:03:28,640 –> 00:03:29,280 you should know.
43 00:03:30,240 –> 00:03:33,520 However, the good thing is, I have a whole series about
44 00:03:33,520 –> 00:03:36,480 start learning mathematics that should help you there.
45 00:03:37,600 –> 00:03:42,400 Now, you don’t have know all the topics there but it would be helpful if you
46 00:03:42,400 –> 00:03:46,960 gather a basic knowledge about logical symbols, set operations and maps.
47 00:03:47,920 –> 00:03:51,760 In particular, working with maps, will be important immediately.
48 00:03:52,880 –> 00:03:55,680 Then, with this knowledge, I would say, you are ready
49 00:03:55,680 –> 00:04:00,400 to start with linear algebra here. Therefore, in the next video,
50 00:04:00,400 –> 00:04:04,240 we can immediately talk about vectors and how to calculate with them.
51 00:04:05,120 –> 00:04:13,840 So I really hope that I see you there. Have a nice day and bye!