What You Will Learn!
- Vector Spaces specifies the no. of independent directions in the space. Infinite dimensional Vector Space are Function spaces in Mathematical Analysis.
- Students can enhance their knowledge in the study of Norms, Inner product Spaces, and other fundamental in mathematical analysis such as Banach & Hilbert spaces
- To understand how students make sense of subspaces of vector spaces in series of in-depth qualitative interviews in technology assisted learning Environment.
- Vector Spaces may be generalized in several ways, leading to more advanced notations in Abstract Algebra also offer a framework for Fourier Expansion.
Description
LINEAR ALGEBRA- Part 2 (VECTOR SPACES)
BASIS AND DIMENSION
Welcome to this 9+ hours of course on Linear Algebra where you will learn the Concept of Vector Spaces , Subspaces of Vector Spaces , Generators of Vectors , Linear Span , Linearly Dependent and Linearly Independent Vectors and Functions. In Linearly dependent and independent vectors and functions you will learn the concept of how to check whether vectors are linearly dependent or not. Furthermore you will learn the conditions of Trivial and Non Trivial Solutions along with Direct Sum of Subspaces.
Then comes the Introduction to Basis and Dimension. In this section, some of the basic concepts in the study of vectors spaces is introduced. Basis is a linearly independent spanning set. The content on Basis for matrices, symmetric matrices, Hermitian Matices, Real Matrices, Columns of Invertible matrices and many more concepts. This course also provides the knowledge about how to find the Dimensions of Vector Spaces and Subspaces. The concept of Coordinate Vector is also included.
This course is also subjected with so many Assignments covering the Definitions, Remarks, Notes , Postulates, with all the Expected Examples and Expected Theorems with Corollary. The assignments will helps you to get grasp of the subject.
Vector Spaces are the subject of Linear Algebra and are well characterized by their dimension , which specifies the number of independent directions in the space. Infinte-Dimensional vector spaces arise naturally in Mathematical Analysis as function spaces, whose vectors are functions.
For any queries related to the course, I would be happy to assist you. Just ping me via Inbox. You will get a course completion certificate after finishing the course.
Who Should Attend!
- Students of mathematics , Physics and Engineering, Graduates and Post Graduates Students.
