Linear Algebra: Table of Contents
Linear Transformation and Matrix. Euclidean vector and euclidean space. Extra: Vector addition is given by parallelogram. Some matrix notations and terminologies. Extra: Matrix transformations are linear. Linear transformation = matrix transformation. Extra: Matrix of a linear transformation. Onto and always existence. Composition and Matrix Multiplication. Extra: Composition of linear transformations is linear. Properties of matrix multiplication. Extra: Criterion for invertibility of a transformation.
Linear Algebra: Description of the Course
Questions for systems of linear equations. It also yields some other results that will be extended to other contexts and more abstract settings. System of linear equations are considered from the geometrical viewpoint of linear transformations. Between euclidean spaces). The existence and uniqueness problems for the equations have natural interpretations ( onto. The matrix operations, especially the matrix product. Matrix, are natrually introduced from the trnasformation viewpoint. And uniqueness ( kernel.