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Complete Linear Algebra for Data Science & Machine Learning
Welcome and Introduction
01 - Welcome & Introduction (2:43)
02 - DETAILED SOLUTIONS of ALL Assignments
Basics of Matrices
03 - Matrices and their Importance (2:07)
04 - Matrix Notation (2:25)
05 - Dimension (Order) of a Matrix (3:20)
06 - Addressing Elements of a Matrix (4:01)
07 - Solving Linear Systems in 2 Unknowns (12:18)
08 - Solving Linear Systems in 3 Unknowns (8:17)
Basics of Matrices (Continued)
09 - IMPORTANT - This section is Optional
10 - Types of Matrices (6:13)
11 - Addition and Subtraction of Matrices (7:38)
12 - Multiplication of Scalars with Matrices (2:16)
13 - Multiplication of two Matrices (18:29)
14 - Inverse and Determinant of a 2x2 Matrix (5:07)
15 - The Formula: Inverse(A) = Adjoint(A) / Determinant(A) (4:12)
16 - EXAMPLE: Calculating Inverse of a 2x2 Matrix (3:22)
17 - Using Matrices to Solve Simultaneous Linear Equations (10:28)
18 - EXAMPLE: Using Matrices to solve Simultaneous Linear Equations (7:40)
19 - CHALLENGE QUESTION: Using Matrices to solve Simultaneous Linear Equations (2:29)
20 - Summary (10:41)
Matrices and Systems of Linear Equations
21 - The Online Matrix Calculator - A FREE Tool (6:20)
22 - Systems of Linear Equations (2x2) (8:38)
23 - Systems of Linear Equations continued (3x3 & more) (6:40)
24 - Elementary Row Operations (10:27)
25 - Row Echelon Form (REF) (10:25)
26 - Reduced Row Echelon Form (RREF) (3:58)
27 - **ASSIGNMENT 1 - Matrices & Linear Equations
Matrix Algebra and Operations
28 - Addition & Subtraction of Matrices (4:09)
29 - Scalar Multiplication with a Matrix (1:44)
30 - Multiplication of two Matrices (10:09)
31 - Transpose of a Matrix (5:14)
32 - **ASSIGNMENT 2 - Matrix Algebra & Operations
Determinant of a Matrix
33 - Determinant of a 2x2 Matrix (5:27)
34 - Determinant of a 3x3 Matrix (12:54)
35 - Computing Determinants quickly using Properties of Determinants (2:14)
36 - **ASSIGNMENT 3 - Determinants
Inverse of a Matrix
37 - Inverse exists ONLY for Square Matrices (4:24)
38 - Singular Matrices (3:58)
39 - Importance of Inverse in solving Linear Systems (6:25)
40 - Inverse of a 2x2 Matrix
41 - Inverse of a 3x3 Matrix - The two methods (2:38)
42 - Inverse of a 3x3 Matrix - Co-factor Method (11:39)
43 - Inverse of a 3x3 Matrix - Gauss-Jordan Elimination Method (17:20)
Properties of Determinants
44 - Properties of Determinants - Row Operation 1 (1:21)
45 - Properties of Determinants - Row Operation 2 (1:38)
46 - Properties of Determinants - Row Operation 3 (1:59)
47 - Properties of Determinants - All Row Operations (1:19)
48 - Properties of Determinants - Row Operations Applied (4:57)
49 - Properties of Determinants - Another Property (3:43)
Introduction to Vectors
50 - Introduction to the Section (0:42)
51 - Scalars and Vectors (5:26)
52 - Geometrical Representation of Vectors (4:35)
53 - Vector Addition & Subtraction (4:31)
54 - Laws of Vector Addition & Head to Tail Rule (10:31)
55 - Unit Vector (6:54)
56 - Components of a Vector in 2D (3:07)
57 - Position Vector (4:25)
58 - 3D Vectors and Magnitude of a Vector (4:42)
59 - Displacement Vector (3:24)
60 - Finding Midpoint using Vectors (4:13)
Vector Spaces
61 - Introduction to Vector Spaces (0:56)
62 - Euclidean Vector Spaces - Part 1 (6:10)
63 - Euclidean Vector Spaces - Part 2 (4:41)
64 - Euclidean Vector Spaces - Part 3 (5:35)
65 - Definition and Closure Properties (5:15)
66 - Axioms of Vector Spaces (4:52)
67 - Example of Closure Properties (5:44)
68 - Example 1 of Vector Spaces (4:34)
69 - Example 2 of Vector Spaces (2:16)
Subspace and Nullspace
70 - Introduction to Subspaces (3:17)
71 - Example 1 of Subspaces (3:32)
72 - Example 2 of Subspaces (3:18)
73 - Example 3 of Subspaces (3:43)
74 - Nullspace of a Matrix (2:24)
75 - Example of Nullspace of a Matrix (8:02)
76 - **ASSIGNMENT 4: Vector Spaces, Subspaces and Null Spaces
Span and Spanning Sets
77 - Span of a set of Vectors (1:54)
78 - Span of a set of Vectors - Example (3:57)
79 - Spanning Set for a Vector Space - Introduction and Examples (4:36)
80 - Spanning Set - Example 3 (5:22)
81 - Spanning Set - Example 4 (4:13)
Linear Dependence and Independence
82 - Introduction to Linear Dependence (9:22)
83 - Definition of Linear Dependence (3:00)
84 - Examples of Linear Dependence (3:44)
85 - More Examples of Linear Dependence (3:34)
86 - A faster method to check Linear Dependency (6:32)
87 - Linear Dependence if X is not a Square Matrix (2:35)
88 - Linear Dependence - Example of a Non-square X Matrix (6:07)
Basis and Dimension
89 - Definition and Example of Basis (4:36)
91 - Dimension of a Vector Space (2:06)
90 - Another Example of Basis (5:34)
92 - Example of Dimension of a Vector Space (3:27)
93 - Standard Basis (2:03)
94 - PRACTICE ACTIVITY
Eigenvalues and Eigenvectors
95 - Introduction to Eigenvalues and Eigenvectors (3:48)
96 - How to Calculate Eigenvalues and Eigenvectors (4:39)
97 - EXAMPLE: Calculating Eigenvalues and Eigenvectors of a 2x2 Matrix (13:52)
Basic Algebra Concepts (Additional Lessons)
98 - Mathematical Operators and their Precedence (BODMAS) (4:03)
99 - Power and Roots (1:52)
100 - Rounding and Estimation (2:36)
101 - Rounding with Decimal Places (2:18)
102 - Rounding with Significant Figures (3:51)
103 - Estimating (1:33)
104 - Fractions, Decimals and Percentages (2:27)
105 - Ratio and Proportion (3:00)
106 - Introduction to the Number System (0:28)
107 - Natural Numbers (1:04)
108 - Whole Numbers (0:34)
109 - Integers (0:44)
110 - Rational Numbers (2:53)
111 - Irrational Numbers (1:41)
112 - EXERCISES (1:06)
113 - Real Numbers (1:04)
114 - Venn Diagram and Flowchart (3:26)
115 - EXAMPLES 1 (5:08)
116 - EXAMPLES 2 (2:45)
117 - EXAMPLE 3 (3:17)
118 - COORDINATE GEOMETRY & STRAIGHT LINES
119 - The Coordinate System (2:53)
120 - The Coordinate System - continued (2:55)
121 - Length of a Line Segment (2:18)
122 - EXAMPLES: Length of a Line Segment (1:59)
123 - EXERCISE: Length of a Line Segment (1:12)
124 - EXAMPLE: Midpoint of a Line Segment (1:03)
125 - EXERCISE: Midpoint of a Line Segment (1:36)
126 - SUMMARY (1:16)
127 - Equation of a Straight Line (5:41)
128 - Gradient of a Straight Line (4:28)
129 - EXAMPLE 1: Equation of a Straight Line (7:32)
130 - EXAMPLE 2: Equation of a Straight Line (5:38)
131 - EXAMPLE 3: Equation of a Straight Line (8:39)
132 - EXERCISES: Equation of a Straight Line (3:45)
133 - Other Forms of Linear Equations (4:25)
134 - A Second Formula for a Straight Line (7:17)
135 - EXERCISE - Using 2nd formula for Linear Equation (3:48)
136 - SUMMARY (2:35)
137 - Equation of a Straight Line (0:47)
138 - Intersection of two Lines (3:06)
139 - EXAMPLE: Intersection of Two Lines (4:03)
140 - EXERCISE: Intersection of Two Lines (1:26)
141 - ACTIVITY 1: Straight Lines (2:07)
142 - ACTIVITY 2: Straight Lines (1:57)
143 - Parallel and Perpendicular Lines (1:48)
144 - EXAMPLES: Parallel and Perpendicular Lines (5:23)
145 - EXERCISES: Parallel and Perpendicular Lines (1:45)
146 - SUMMARY (1:41)
Basic Algebra Concepts (Additional Lessons) 2
147 - FUNCTIONS, GRAPHS & TRANSFORMATIONS
148 - Introduction to Functions (5:24)
149 - Graphs of Common Functions (5:09)
150 - Straight Lines (3:51)
151 - Graph of a Linear Function (2:08)
152 - Validation of Graphs as Functions (4:29)
153 - Library of Functions (5:51)
154 - Introduction to Asymptotes (7:38)
155 - Limits (4:30)
156 - ACTIVITY: Memorize these Graphs (0:33)
157 - Translations - Vertical Shift (8:47)
158 - Translations - Horizontal Shift (7:08)
159 - ACTIVITY: Translations (5:19)
160 - SUMMARY - Translations (4:38)
161 - EXERCISE: Translations (7:16)
162 - Transformations - Stretching and Compression (4:29)
163 - ACTIVITY: Transformations (2:52)
164 - EXERCISE: Transformations (3:32)
165 - SUMMARY-Stretches and Compression (3:12)
166 - SUMMARY - Translations and Transformations (5:51)
167 - Reflection about X-axis and Y-axis (8:46)
168 - SUMMARY: Reflections (1:23)
169 - EXERCISE: Sketching Complex Graphs (16:08)
170 - SUMMARY (2:52)
171 - Common Graphs (3:31)
172 - Basic Types of Graph Manipulations (1) (3:08)
173 - Basic Types of Graph Manipulations (2) (7:03)
174 - EXAMPLE: Manipulation of Graphs (7:11)
175 - Congratulations on Successfully Completing the Course (1:49)
76 - **ASSIGNMENT 4: Vector Spaces, Subspaces and Null Spaces
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