Linear Algebra Crash Course

Linear Systems of any kind. Matrix Operations and Determinants .Vector Spaces in Linear Algebra
Rating: 4.6 out of 5 (421 ratings)
9,519 students
Linear Algebra Crash Course
Rating: 4.6 out of 5 (421 ratings)
9,521 students
Solve any linear system
Solve linear systems with parameters
Solve linear systems with different numbers of variables and equations
Know what is a Vector Space
Determine if some vectors are dependent or not
Linear combinations of vectors
Check if a set of vectors is a base
Know what are the coordinates of a vector in a given space

Requirements

  • Be able to do basic Mathematical operations
  • Solve simple equations like 3x +7 = 5 (x= - 2/3)
Description

Learn the fundamentals of Linear Algebra.

Linear Algebra fundamentals are: Linear Systems, Matrix Algebra and  Vector Spaces.

Without these 3 pillars it is impossible to grasp the complex subject of linear algebra. This course specializes exactly on that:  Linear Systems Matrix Algebra and Vector Spaces.

This is what you will learn in this course:

What is a linear System

Triangular System and why they are important

What operation you are allowed to perform on any system

Solve systems with a parameter

Solve any linear System, with different number of variables and equations

________________________________________________________

Matrices

Matrix Algebra:  Sum, Difference and Multiplications

Transpose of a Matrix

Symmetric Matrices

Inverse of a Matrix and how to compute one

Determinant of Matrices and their properties

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Vectors, sum, difference and properties

Vector spaces, example and non examples

Linear combinations of Vectors

Span of Vectors

What is a base of a Vector Space, coordinates of vectors.

Who this course is for:
  • Anyone interested in Linear Algebra
  • People interested in a solid background for Linear Algebra
  • People interested in solving very general Linear Systems
  • People interested in Knowing about Vector Spaces
Course content
12 sections • 106 lectures • 8h 6m total length
  • Introduction
    03:02
  • The Simplest Linear System: 1 Equation
    04:34
  • 2 Equations Lin. System- How many solutions?
    09:12
  • Why Linear?
    01:25
  • General Linear System ( n Equations )
    04:29
  • Matrix Form of Linear Systems
    03:42
  • Triangular Systems ( Important ! )
    05:57
  • Methods to Solve L.S.
    03:20
  • Elimination Method Fast Overview
    02:03
  • Permitted Change on a L.S.
    06:52
  • Elimination Method Guide
    02:41
  • Our First System Solved
    05:17
  • 3 x 3 system
    07:44
  • All Possible Cases
    06:47
  • Systems with Parameters
    12:38
  • How to Procede (Useful for big Systems)
    04:31
  • Avoid Confusion in Solving L.S.
    04:33
  • Infinite many Solutions in systems
    10:00
  • Exercise: Lin. Syst. Solutions
    00:11
  • Solution of the previous Exercises
    10:08
  • Exercise 3x3 With Parameter
    00:12
  • Solution Ex. 3x3 With Parameter
    07:20
  • Beyond Linear Algebra...
    01:00
  • Intro to mxn Systems (Different number of Equations and Variables)
    07:43
  • Solution of mxn Systems
    02:08
  • Guide to mxn Systems
    08:54
  • Example mxn System Solved in details. 1
    05:13
  • Example 2. mxn System Solved in details.
    05:01
  • Matrix Overview
    01:54
  • Matrix Definition and examples
    05:25
  • Matrix Basic Operations
    06:16
  • Diagonal Matrices
    06:13
  • Matrix components
    04:20
  • Exercise Matrix 1
    00:00
  • Solution Exercise Matrix 1
    02:44
  • Exercise Matrix 2
    00:00
  • Solution Exercise Matrix 2
    04:04
  • Exercise Matrix 3: Components
    00:00
  • Solution Exercise Matrix 3: Components
    03:41
  • Matrix Multiplication
    02:33
  • Matrix Multiplication-2
    06:58
  • Matrix Associative Property
    03:57
  • Matrix Distribution Property
    04:24
  • Linear Systems and Matrices
    08:47
  • Exercise Matrix 3
    00:00
  • Solution Exercise Matrix 3
    04:24
  • Exercise Matrix 4
    00:00
  • Solution Exercise Matrix 4
    05:03
  • Exercise Matrix 5
    00:00
  • Solution Exercise Matrix 5
    02:28
  • Exercise Matrix 6: Lin. Syst.
    00:00
  • Solution Exercise Matrix 6: Lin. Syst.
    02:17
  • Transpose Matrix
    04:20
  • Symmetric Matrix
    04:33
  • Inverse Matrix-1
    08:06
  • Inverse Matrix-2
    09:27
  • Inverse Matrix-3
    04:00
  • Inverse Matrix-4
    01:22
  • Exercise Matrix 7 Transpose
    00:00
  • Solution Exercise Matrix 7 Transpose
    02:57
  • Exercise Matrix 8: Inverse
    00:00
  • Solution Exercise Matrix 8: Inverse
    03:52
  • Exercise Matrix 9: Inverse
    00:00
  • Solution Exercise Matrix 9: Inverse
    05:52
  • Solution Exercise Matrix 9 -Part 2
    02:14
  • Determinant
    08:37
  • Determinant 3x3
    04:23
  • Determinant 4x4
    05:30
  • General computation of Determinants
    06:32
  • Properties of Determinants
    06:05
  • Determinants of Triangular Matrices
    01:47
  • Vectors: Introduction
    05:15
  • Sum of Vectors
    09:55
  • Difference of Vectors
    04:45
  • Vector Base
    06:39
  • Vector Components
    07:11
  • The Line, The Plane, The Space....
    06:32
  • Properties of R^n
    06:41
  • Vector Space Definition
    12:49
  • Example of Vector Spaces
    05:36
  • Abstract Vector Spaces: Polinomials
    05:10
  • Non Vector Spaces
    08:09
  • Vector Subspaces
    05:08
  • Exercise Vector Space
    00:11
  • Solution to Exercise
    04:28
  • Linear Combination of Vectors
    08:38
  • Vector Span
    05:12
  • Span Example
    10:10
  • More Details about Span
    06:54
  • Linear Dependent and Independent Vector
    06:26
  • Linear Dependent Vectors: Examples
    05:35
  • Exercise 2
    00:02
  • Solution to Exercise 2
    05:06

Instructor
Francesco Santi
  • 4.6 Instructor Rating
  • 3,410 Reviews
  • 22,272 Students
  • 5 Courses

Francesco Santi is a Phd Researcher and Consultant in data analysis and strategic planning .

He holds a  Phd in Applied Mathematics 

With nearly 10 years of programming experience he has developed since the very start a Passion for Teaching and Consulting.

Nowadays he specializes in using his technical knowledge in business related topic such as data analysis for small business and data analysis for strategic planning