This course on Matrix Algebra for Engineers teaches Matrix Algebra for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile, it’s available in language.
This course on Matrix Algebra for Engineers teaches Matrix Algebra for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile. This complete course is available in language.
Learn new concepts from professionals in the field.
Acquire a basic understanding of a topic or skill
Gain practical project experience to enhance employability.
Obtain a career certificate that can be shared.
Topics you will learn
MATRICES
10 videos
Week One Introduction
Definition of a Matrix | Lecture 1
Addition and Multiplication of Matrices | Lecture 2
Special Matrices | Lecture 3
Transpose Matrix | Lecture 4
Inner and Outer Products | Lecture 5
Inverse Matrix | Lecture 6
Orthogonal Matrices | Lecture 7
Rotation Matrices | Lecture 8
Permutation Matrices | Lecture 9
27 readings
Welcome and Course Information
Certificate or Audit?
How to Write Math in the Discussion Forums Using MathJax
Construct Some Matrices
Matrix Addition and Multiplication
AB=AC Does Not Imply B=C
Matrix Multiplication Does Not Commute
Associative Law for Matrix Multiplication
AB=0 When A and B Are Not zero
Product of Diagonal Matrices
Product of Triangular Matrices
Transpose of a Matrix Product
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix
Construction of a Square Symmetric Matrix
Example of a Symmetric Matrix
Sum of the Squares of the Elements of a Matrix
Inverses of Two-by-Two Matrices
Inverse of a Matrix Product
Inverse of the Transpose Matrix
Uniqueness of the Inverse
Determinant as an Area
Product of Orthogonal Matrices
The Identity Matrix is Orthogonal
Inverse of the Rotation Matrix
Three-dimensional Rotation
Three-by-Three Permutation Matrices
Inverses of Three-by-Three Permutation Matrices
6 quizzes
Week One Assessment
Diagnostic Quiz
Matrix Definitions
Transposes and Inverses
Orthogonal Matrices
Week One Assessment (audit)
SYSTEMS OF LINEAR EQUATIONS
7 videos
Week Two Introduction
Gaussian Elimination | Lecture 10
Reduced Row Echelon Form | Lecture 11
Computing Inverses | Lecture 12
Elementary Matrices | Lecture 13
LU Decomposition | Lecture 14
Solving (LU)x = b | Lecture 15
6 readings
Gaussian Elimination
Reduced Row Echelon Form
Computing Inverses
Elementary Matrices
LU Decomposition
Solving (LU)x = b
4 quizzes
Week Two Assessment
Gaussian Elimination
LU Decomposition
Week Two Assessment (audit)
VECTOR SPACES
13 videos
Week Three Introduction
Vector Spaces | Lecture 16
Linear Independence | Lecture 17
Span, Basis and Dimension | Lecture 18
Gram-Schmidt Process | Lecture 19
Gram-Schmidt Process Example | Lecture 20
Null Space | Lecture 21
Application of the Null Space | Lecture 22
Column Space | Lecture 23
Row Space, Left Null Space and Rank | Lecture 24
Orthogonal Projections | Lecture 25
The Least-Squares Problem | Lecture 26
Solution of the Least-Squares Problem | Lecture 27
14 readings
Zero Vector
Examples of Vector Spaces
Linear Independence
Orthonormal basis
Gram-Schmidt Process
Gram-Schmidt on Three-by-One Matrices
Gram-Schmidt on Four-by-One Matrices
Null Space
Underdetermined System of Linear Equations
Column Space
Fundamental Matrix Subspaces
Orthogonal Projections
Setting Up the Least-Squares Problem
Line of Best Fit
6 quizzes
Week Three Assessment
Vector Space Definitions
Gram-Schmidt Process
Fundamental Subspaces
Orthogonal Projections
Week Three Assessment (audit)
EIGENVALUES AND EIGENVECTORS
13 videos
Week Four Introduction
Two-by-Two and Three-by-Three Determinants | Lecture 28
Laplace Expansion | Lecture 29
Leibniz Formula | Lecture 30
Properties of a Determinant | Lecture 31
The Eigenvalue Problem | Lecture 32
Finding Eigenvalues and Eigenvectors (Part A) | Lecture 33
Finding Eigenvalues and Eigenvectors (Part B) | Lecture 34
Matrix Diagonalization | Lecture 35
Matrix Diagonalization Example | Lecture 36
Powers of a Matrix | Lecture 37
Powers of a Matrix Example | Lecture 38
Concluding Remarks
20 readings
Determinant of the Identity Matrix
Row Interchange
Determinant of a Matrix Product
Compute Determinant Using the Laplace Expansion
Compute Determinant Using the Leibniz Formula
Determinant of a Matrix With Two Equal Rows
Determinant is a Linear Function of Any Row
Determinant Can Be Computed Using Row Reduction
Compute Determinant Using Gaussian Elimination
Characteristic Equation for a Three-by-Three Matrix
Eigenvalues and Eigenvectors of a Two-by-Two Matrix
Eigenvalues and Eigenvectors of a Three-by-Three Matrix
Complex Eigenvalues
Linearly Independent Eigenvectors
Invertibility of the Eigenvector Matrix
Diagonalize a Three-by-Three Matrix
Matrix Exponential
Powers of a Matrix
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Acknowledgements
5 quizzes
Week Four Assessment
Determinants
The Eigenvalue Problem
Matrix Diagonalization
Week Four Assessment (audit)
Course Offerings
Certificate you will get
Certificate Features
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Pre Requsites
Curious Mind to learn new concepts
Strong internet connection
After this Course
Course is for
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FAQ's
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