Linear Transformation Examples: Rotations in R2 Linear Transformation Examples: Rotations in R2
Linear Transformation Examples: Scaling and Reflections Creating scaling and reflection ...
More on Matrix Addition and Scalar Multiplication More on Matrix Addition and Scalar ...
Sums and Scalar Multiples of Linear Transformations Sums and Scalar Multiples of Linear ...
Preimage and Kernel Example Example involving the preimage of a set under a transformation. ...
Preimage of a set Definition of preimage of a set
im(T): Image of a Transformation Showing that the image of a subspace under a transformation ...
Image of a subset under a transformation Exploring what happens to a subset of the domain ...
Linear Transformations as Matrix Vector Products Showing how ANY linear transformation can be ...
Matrix Vector Products as Linear Transformations Matrix Vector Products as Linear Transformations
Linear Transformations Introduction to linear transformations
Vector Transformations Introduction to the notion of vector transformations
A more formal understanding of functions A more formal understanding of functions
Showing that the candidate basis does span C(A) Showing that just the columns of A associated ...
Showing relation between basis cols and pivot cols Showing that linear independence of pivot ...
Dimension of the Column Space or Rank Dimension of the Column Space or Rank
Dimension of the Null Space or Nullity Dimension of the Null Space or Nullity
Proof: Any subspace basis has same number of elements Proof: Any subspace basis has same ...
Visualizing a Column Space as a Plane in R3 Determining the planar equation for a column ...
Null Space and Column Space Basis Figuring out the null space and a basis of a column space ...
Column Space of a Matrix Introduction to the column space of a matrix
Null Space 3: Relation to Linear Independence Understanding how the null space of a matrix ...
Null Space 2: Calculating the null space of a matrix Calculating the null space of a matrix
Introduction to the Null Space of a Matrix Showing that the Null Space of a Matrix is a valid ...