Khan Academy: Linear Transformation Examples: Unit Vectors

A video showing how any linear transformation can be represented as a matrix vector product.

Expressing a Projection on to a line as a Matrix Vector prod

Construction a rotation transformation in R3 around the x-axis.

Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...

Video gives examples of vector addition, graphing vectors, multiplying vectors by a scalar and vector subtraction using vectors in R2 and extends to vectors in other dimensions. [25:33]

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...

Video first gives the conditions that define a linear transformation. Gives examples of determining if a transformation is linear or not. Shows several types of notation for vector transformations. [13:52]

Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...