Linear Algebra Part 4 : Vector Spaces and Subspaces

Linear Algebra, mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations. In this 3hr 54 min Course ' Linear Algebra Part 4 Echelon Matrix and Normal Form of Matrix' is having very interesting contents based on Echelon Matrix, Row Column Operations on matrix, Rank of Matrix, Normal Form of Matrix, and Determining the Non singular Matrices.

The listed Contents of the Course 'Echelon Matrix & Normal Form of Matrix'

1) The introduction to the Echelon Matrix and its definition with examples.

2) Finding the Basis and Dimension of subspaces.

3) Finding basis and dimension of the sum of subspaces.

4) Finding the basis and dimension of intersection of subspaces.

5) Finding the basis and dimension of subspaces having vectors as matrices.

6) Finding the basis and dimension of subspaces having vectors as real polynomials of degree less than equal to 3 including the zero polynomial.

7) Finding the basis and dimension of subspaces, having vectors as xy-plane or x axis or respective other axis and planes.

8) Finding the basis and dimension  of subspaces, sum of subspaces, intersection of subspaces with determination of rank too.

9) Equivalence of row column operations on matrices.

10) Normal form of matrix introduction with examples

11) Determining the rank of matrix by reducing the given matrix into its normal form.

12)Determining the non singular matrices P and Q by reducing the given matrix into its normal form such that PAQ is in normal form where A is the given matrix.

Including all Important Theorems and Proofs with Solved Examples and assignments plus Practice Questions.