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Linear Algebra
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Total Videos :143
Introduction to matrices
00:11:51
Matrix multiplication (part 1)
00:13:40
Matrix multiplication (part 2)
00:14:37
Inverse Matrix (part 1)
00:14:14
Inverting matrices (part 2)
00:16:44
Inverting Matrices (part 3)
00:13:36
Matrices to solve a system of equations
00:16:32
Matrices to solve a vector combination problem
00:14:20
Singular Matrices
00:14:27
3-variable linear equations (part 1)
00:08:01
Solving 3 Equations with 3 Unknowns
00:15:26
Linear Algebra: Introduction to Vectors
00:16:31
Linear Algebra: Vector Examples
00:25:33
Linear Algebra: Parametric Representations of Lines
00:24:46
Linear Combinations and Span
00:20:35
Linear Algebra: Introduction to Linear Independence
00:15:46
More on linear independence
00:17:38
Span and Linear Independence Example
00:16:53
Linear Subspaces
00:23:29
Linear Algebra: Basis of a Subspace
00:19:00
Vector Dot Product and Vector Length
00:09:10
Proving Vector Dot Product Properties
00:10:45
Proof of the Cauchy-Schwarz Inequality
00:16:55
Linear Algebra: Vector Triangle Inequality
00:18:53
Defining the angle between vectors
00:25:11
Defining a plane in R3 with a point and normal vector
00:13:53
Linear Algebra: Cross Product Introduction
00:15:47
Proof: Relationship between cross product and sin of angle
00:18:09
Dot and Cross Product Comparison/Intuition
00:19:14
Matrices: Reduced Row Echelon Form 1
00:17:43
Matrices: Reduced Row Echelon Form 2
00:07:37
Matrices: Reduced Row Echelon Form 3
00:12:08
Matrix Vector Products
00:21:10
Introduction to the Null Space of a Matrix
00:10:23
Null Space 2: Calculating the null space of a matrix
00:13:07
Null Space 3: Relation to Linear Independence
00:11:35
Column Space of a Matrix
00:10:40
Null Space and Column Space Basis
00:25:13
Visualizing a Column Space as a Plane in R3
00:21:11
Proof: Any subspace basis has same number of elements
00:21:35
Dimension of the Null Space or Nullity
00:13:59
Dimension of the Column Space or Rank
00:12:48
Showing relation between basis cols and pivot cols
00:08:33
Showing that the candidate basis does span C(A)
00:13:40
A more formal understanding of functions
00:16:01
Vector Transformations
00:14:19
Linear Transformations
00:13:52
Matrix Vector Products as Linear Transformations
00:17:04
Linear Transformations as Matrix Vector Products
00:17:32
Image of a subset under a transformation
00:18:11
im(T): Image of a Transformation
00:16:37
Preimage of a set
00:05:23
Preimage and Kernel Example
00:15:23
Sums and Scalar Multiples of Linear Transformations
00:15:09
More on Matrix Addition and Scalar Multiplication
00:10:41
Linear Transformation Examples: Scaling and Reflections
00:15:13
Linear Transformation Examples: Rotations in R2
00:17:52
Rotation in R3 around the X-axis
00:12:18
Unit Vectors
00:06:59
Introduction to Projections
00:14:37
Expressing a Projection on to a line as a Matrix Vector prod
00:16:40
Compositions of Linear Transformations 1
00:12:21
Compositions of Linear Transformations 2
00:16:30
Linear Algebra: Matrix Product Examples
00:18:14
Matrix Product Associativity
00:11:59
Distributive Property of Matrix Products
00:09:52
Linear Algebra: Introduction to the inverse of a function
00:18:53
Proof: Invertibility implies a unique solution to f(x)=y
00:22:41
Surjective (onto) and Injective (one-to-one) functions
00:09:31
Relating invertibility to being onto and one-to-one
00:06:31
Determining whether a transformation is onto
00:25:51
Linear Algebra: Exploring the solution set of Ax=b
00:16:34
Linear Algebra: Matrix condition for one-to-one trans
00:19:59
Linear Algebra: Simplifying conditions for invertibility
00:06:37
Linear Algebra: Showing that Inverses are Linear
00:21:25
Linear Algebra: Deriving a method for determining inverses
00:18:00
Linear Algebra: Example of Finding Matrix Inverse
00:06:22
Linear Algebra: Formula for 2x2 inverse
00:18:20
Linear Algebra: 3x3 Determinant
00:10:01
Linear Algebra: nxn Determinant
00:18:40
Linear Algebra: Determinants along other rows/cols
00:09:03
Linear Algebra: Rule of Sarrus of Determinants
00:07:18
Linear Algebra: Determinant when row multiplied by scalar
00:13:20
Linear Algebra: (correction) scalar muliplication of row
00:02:52
Linear Algebra: Determinant when row is added
00:16:55
Linear Algebra: Duplicate Row Determinant
00:08:19
Linear Algebra: Determinant after row operations
00:10:25
Linear Algebra: Upper Triangular Determinant
00:08:07
Linear Algebra: Simpler 4x4 determinant
00:09:13
Linear Algebra: Determinant and area of a parallelogram
00:21:37
Linear Algebra: Determinant as Scaling Factor
00:20:09
Linear Algebra: Transpose of a Matrix
00:08:37
Linear Algebra: Determinant of Transpose
00:14:10
Linear Algebra: Transpose of a Matrix Product
00:08:50
Linear Algebra: Transposes of sums and inverses
00:08:41
Linear Algebra: Transpose of a Vector
00:12:06
Linear Algebra: Rowspace and Left Nullspace
00:23:18
Lin Alg: Visualizations of Left Nullspace and Rowspace
00:19:50
Linear Algebra: Orthogonal Complements
00:22:08
Linear Algebra: Rank(A) = Rank(transpose of A)
00:11:13
Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
00:09:27
Lin Alg: Representing vectors in Rn using subspace members
00:27:00
Lin Alg: Orthogonal Complement of the Orthogonal Complement
00:12:18
Lin Alg: Orthogonal Complement of the Nullspace
00:03:27
Lin Alg: Unique rowspace solution to Ax=b
00:19:12
Linear Alg: Rowspace Solution to Ax=b example
00:19:38
Lin Alg: Showing that A-transpose x A is invertible
00:12:34
Linear Algebra: Projections onto Subspaces
00:17:26
Linear Alg: Visualizing a projection onto a plane
00:09:28
Lin Alg: A Projection onto a Subspace is a Linear Transforma
00:16:15
Linear Algebra: Subspace Projection Matrix Example
00:13:04
Lin Alg: Another Example of a Projection Matrix
00:21:35
Linear Alg: Projection is closest vector in subspace
00:09:05
Linear Algebra: Least Squares Approximation
00:15:32
Linear Algebra: Least Squares Examples
00:18:50
Linear Algebra: Another Least Squares Example
00:13:25
Linear Algebra: Coordinates with Respect to a Basis
00:16:08
Linear Algebra: Change of Basis Matrix
00:17:55
Lin Alg: Invertible Change of Basis Matrix
00:13:34
Lin Alg: Transformation Matrix with Respect to a Basis
00:18:02
Lin Alg: Alternate Basis Tranformation Matrix Example
00:13:20
Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
00:12:36
Lin Alg: Changing coordinate systems to help find a transformation matrix
00:28:59
Linear Algebra: Introduction to Orthonormal Bases
00:11:16
Linear Algebra: Coordinates with respect to orthonormal bases
00:15:28
Lin Alg: Projections onto subspaces with orthonormal bases
00:16:14
Lin Alg: Finding projection onto subspace with orthonormal basis example
00:06:42
Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix
00:27:04
Lin Alg: Orthogonal matrices preserve angles and lengths
00:11:16
Linear Algebra: The Gram-Schmidt Process
00:19:24
Linear Algebra: Gram-Schmidt Process Example
00:13:14
Linear Algebra: Gram-Schmidt example with 3 basis vectors
00:13:57
Linear Algebra: Introduction to Eigenvalues and Eigenvectors
00:07:43
Linear Algebra: Proof of formula for determining Eigenvalues
00:09:19
Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix
00:05:39
Linear Algebra: Finding Eigenvectors and Eigenspaces example
00:14:34
Linear Algebra: Eigenvalues of a 3x3 matrix
00:14:08
Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix
00:15:34
Linear Algebra: Showing that an eigenbasis makes for good coordinate systems
00:13:09
Vector Triple Product Expansion (very optional)
00:14:25
Normal vector from plane equation
00:09:58
Point distance to plane
00:12:12
Distance Between Planes
00:14:45
Linear Algebra
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Total Videos :143
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First Video of Linear Algebra
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Introduction to matrices
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