LECTURES

• 1.Introduction to matrices
• 2.Matrix multiplication (part 1)
• 3.Matrix multiplication (part 2)
• 4.Inverse Matrix (part 1)
• 5.Inverting matrices (part 2)
• 6.Inverting Matrices (part 3)
• 7.Matrices to solve a system of equations
• 8.Matrices to solve a vector combination problem
• 9.Singular Matrices
• 10.3-variable linear equations (part 1)
• 11.Solving 3 Equations with 3 Unknowns
• 12.Linear Algebra Introduction to Vectors
• 13.Linear Algebra Vector Examples
• 14.Linear Algebra Parametric Representations of Lines
• 15.Linear Combinations and Span
• 16.Linear Algebra Introduction to Linear Independence
• 17.More on linear independence
• 18.Span and Linear Independence Example
• 19.Linear Subspaces
• 20.Linear Algebra Basis of a Subspace
• 21.Vector Dot Product and Vector Length
• 22.Proving Vector Dot Product Properties
• 23.Proof of the Cauchy-Schwarz Inequality
• 24.Linear Algebra Vector Triangle Inequality
• 25.Defining the angle between vectors
• 26.Defining a plane in R3 with a point and normal vector
• 27.Linear Algebra Cross Product Introduction
• 28.Proof Relationship between cross product and sin of angle
• 29.Dot and Cross Product ComparisonIntuition
• 30.Matrices Reduced Row Echelon Form 1
• 31.Matrices Reduced Row Echelon Form 2
• 32.Matrices Reduced Row Echelon Form 3
• 33.Matrix Vector Products
• 34.Introduction to the Null Space of a Matrix
• 35.Null Space 2 Calculating the null space of a matrix
• 36.Null Space 3 Relation to Linear Independence
• 37.Column Space of a Matrix
• 38.Null Space and Column Space Basis
• 39.Visualizing a Column Space as a Plane in R3
• 40.Proof Any subspace basis has same number of elements
• 41.Dimension of the Null Space or Nullity
• 42.Dimension of the Column Space or Rank
• 43.Showing relation between basis cols and pivot cols
• 44.Showing that the candidate basis does span C(A)
• 45.A more formal understanding of functions
• 46.Vector Transformations
• 47.Linear Transformations
• 48.Matrix Vector Products as Linear Transformations
• 49.Linear Transformations as Matrix Vector Products
• 50.Image of a subset under a transformation