Become a Linear Algebra Master

Become a Linear Algebra Master
Become a Linear Algebra Master
English | MP4 | AVC 1280×720 | AAC 48KHz 2ch | 15 Hours | 4.00 GB

Learn everything from Linear Algebra, then test your knowledge with 400+ practice questions

This course includes video and text explanations of everything from Linear Algebra, and it includes quizzes (with solutions!) and an additional workbooks with extra practice problems, to help you test your understanding along the way. Become a Linear Algebra Master is organized into the following sections:

What you’ll learn

  • Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
  • Operations on two matrices, including matrix multiplication and elimination matrices
  • Matrices as vectors, including linear combinations and span, linear independence, and subspaces
  • Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
  • Matrix-vector products, including the null and column spaces, and solving Ax=b
  • Transformations, including linear transformations, projections, and composition of transformations
  • Inverses, including invertible and singular matrices, and solving systems with inverse matrices
  • Determinants, including upper and lower triangular matrices, and Cramer’s rule
  • Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
  • Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
  • Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process
  • Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
Table of Contents

Getting started
1 Hi! START HERE: Course overview
2 Download the formula sheet

Operations on one matrix
3 Introduction to operations on one matrix
4 RESOURCE: Quiz solutions for this section
5 Linear systems in two unknowns
6 Linear systems in two unknowns
7 Linear systems in three unknowns
8 Linear systems in three unknowns
9 Matrix dimensions and entries
10 Matrix dimensions and entries
11 Representing systems with matrices
12 Representing systems with matrices
13 Simple row operations
14 Simple row operations
15 Pivot entries and row-echelon forms
16 Pivot entries and row-echelon forms
17 Gauss-Jordan elimination
18 Gauss-Jordan elimination
19 Number of solutions to the linear system
20 Number of solutions to the linear system
21 BONUS! Extra practice problems. 🙂

Operations on two matrices
22 Introduction to operations on two matrices
23 RESOURCE: Quiz solutions for this section
24 Matrix addition and subtraction
25 Matrix addition and subtraction
26 Scalar multiplication
27 Scalar multiplication
28 Zero matrices
29 Zero matrices
30 Matrix multiplication
31 Matrix multiplication
32 Identity matrices
33 Identity matrices
34 The elimination matrix
35 The elimination matrix
36 BONUS! Extra practice problems. 🙂

Matrices as vectors
37 Introduction to matrices as vectors
38 RESOURCE: Quiz solutions for this section
39 Vectors
40 Vectors
41 Vector operations
42 Vector operations
43 Unit vectors and basis vectors
44 Unit vectors and basis vectors
45 Linear combinations and span
46 Linear combinations and span
47 Linear independence in two dimensions
48 Linear independence in two dimensions
49 Linear independence in three dimensions
50 Linear independence in three dimensions
51 Linear subspaces
52 Linear subspaces
53 Spans as subspaces
54 Spans as subspaces
55 Basis
56 Basis
57 BONUS! Extra practice problems. 🙂

Dot products and cross products
58 Introduction to dot products and cross products
59 RESOURCE: Quiz solutions for this section
60 Dot products
61 Dot products
62 Cauchy-Schwarz inequality
63 Cauchy-Schwarz inequality
64 Vector triangle inequality
65 Vector triangle inequality
66 Angle between vectors
67 Angle between vectors
68 Equation of a plane, and normal vectors
69 Equation of a plane, and normal vectors
70 Cross products
71 Cross products
72 Dot and cross products as opposite ideas
73 Dot and cross products as opposite ideas
74 BONUS! Extra practice problems. 🙂

Matrix-vector products
75 Introduction to matrix-vector products
76 RESOURCE: Quiz solutions for this section
77 Multiplying matrices by vectors
78 Multiplying matrices by vectors
79 The null space and Ax=O
80 The null space and Ax=O
81 Null space of a matrix
82 Null space of a matrix
83 The column space and Ax=b
84 The column space and Ax=b
85 Solving Ax=b
86 Solving Ax=b
87 Dimensionality, nullity, and rank
88 Dimensionality, nullity, and rank
89 BONUS! Extra practice problems. 🙂

Transformations
90 Introduction to transformations
91 RESOURCE: Quiz solutions for this section
92 Functions and transformations
93 Functions and transformations
94 Transformation matrices and the image of the subset
95 Transformation matrices and the image of the subset
96 Preimage, image, and the kernel
97 Preimage, image, and the kernel
98 Linear transformations as matrix-vector products
99 Linear transformations as matrix-vector products
100 Linear transformations as rotations
101 Linear transformations as rotations
102 Adding and scaling linear transformations
103 Adding and scaling linear transformations
104 Projections as linear transformations
105 Projections as linear transformations
106 Compositions of linear transformations
107 Compositions of linear transformations
108 BONUS! Extra practice problems. 🙂

Inverses
109 Introduction to inverses
110 RESOURCE: Quiz solutions for this section
111 Inverse of a transformation
112 Inverse of a transformation
113 Invertibility from the matrix-vector product
114 Invertibility from the matrix-vector product
115 Inverse transformations are linear
116 Inverse transformations are linear
117 Matrix inverses, and invertible and singular matrices
118 Matrix inverses, and invertible and singular matrices
119 Solving systems with inverse matrices
120 Solving systems with inverse matrices
121 BONUS! Extra practice problems. 🙂

Determinants
122 Introduction to determinants
123 RESOURCE: Quiz solutions for this section
124 Determinants
125 Determinants
126 Cramer’s rule for solving systems
127 Cramer’s rule for solving systems
128 Modifying determinants
129 Modifying determinants
130 Upper and lower triangular matrices
131 Upper and lower triangular matrices
132 Using determinants to find area
133 Using determinants to find area
134 BONUS! Extra practice problems. 🙂

Transposes
135 Introduction to transposes
136 RESOURCE: Quiz solutions for this section
137 Transposes and their determinants
138 Transposes and their determinants
139 Transposes of products, sums, and inverses
140 Transposes of products, sums, and inverses
141 Null and column spaces of the transpose
142 Null and column spaces of the transpose
143 The product of a matrix and its transpose
144 The product of a matrix and its transpose
145 BONUS! Extra practice problems. 🙂

Orthogonality and change of basis
146 Introduction to orthogonality and change of basis
147 RESOURCE: Quiz solutions for this section
148 Orthogonal complements
149 Orthogonal complements
150 Orthogonal complements of the fundamental subspaces
151 Orthogonal complements of the fundamental subspaces
152 Projection onto the subspace
153 Projection onto the subspace
154 Least squares solution
155 Least squares solution
156 Coordinates in a new basis
157 Coordinates in a new basis
158 Transformation matrix for a basis
159 Transformation matrix for a basis
160 BONUS! Extra practice problems. 🙂

Orthonormal bases and Gram-Schmidt
161 Introduction to orthonormal bases and Gram-Schmidt
162 RESOURCE: Quiz solutions for this section
163 Orthonormal bases
164 Orthonormal bases
165 Projection onto an orthonormal basis
166 Projection onto an orthonormal basis
167 Gram-Schmidt process for change of basis
168 Gram-Schmidt process for change of basis
169 BONUS! Extra practice problems. 🙂

Eigenvalues and Eigenvectors
170 Introduction to Eigenvalues and Eigenvectors
171 RESOURCE: Quiz solutions for this section
172 Eigenvalues, eigenvectors, eigenspaces
173 Eigenvalues, eigenvectors, eigenspaces
174 Eigen in three dimensions
175 Eigen in three dimensions
176 BONUS! Extra practice problems. 🙂

Final exam and wrap-up
177 Linear Algebra final exam
178 Wrap-up