Introduction In mathematics, particularly in linear algebra and functional analysis, the concepts of inner product and inner product space play a crucial role in generalizing geometric ideas like length, angle, and orthogonality to more abstract settings. These concepts are foundational in fields such as Read More …
Category: Linear Algebra
Eigen Values of Similar Matrices | Linear Algebra
Introduction Two matrices, say A and B, are called similar if there exists an invertible matrix P such that: B=P−1AP This means that B is essentially a transformed version of A. But here’s the cool part: even though A and B might look different, they share something very special—their eigenvalues!” Eigenvalues are those Read More …
How to find the basis of a vector space V?
How to find the basis of a vector space? How to find the basis of a vector space V? In order to find the basis of a vector space , we need to check two properties: The vectors should be Read More …
Complete List of Linear Algebra Video Lectures 2024
Here is the Complete List of Linear Algebra Course: Lesson 1: Matrix Basic Operation Lesson 2: Properties of determinant with example https://www.youtube.com/watch?v=Xl1FV6EVIQE&list=PLacdleb4rX6-ROG5FT-ijn74jRtrszIU4&index=40&pp=gAQBiAQB Lesson 3: Nodal Incident matrices for networks Lesson 4: Solving system of linear equations using Gauss Elimination https://www.youtube.com/watch?v=Q_NHw_RZsZs&list=PLacdleb4rX6-ROG5FT-ijn74jRtrszIU4&index=7&pp=gAQBiAQB Read More …
What is the Gram Schmidt Procedure? Explanation and Example
Since, by applying head to tail rule on the vectors components, we can generate the original vector A. After that we need to find the projections of one vector to another vector. This projection is subtracted from the other vector and hence these two vectors become orthogonal.
So, for two vectors A and B lets say we want to generate a new set of vectors W and Y that will be orthogonal to each other. We will assume
What are the Properties of Determinant?
Properties of Determinant In this article, I have discussed some of the properties of determinant. Determinants are mathematical objects that are associated with square matrices. They have several properties that make them useful in various mathematical applications. Here are some Read More …
How to test that the Given Vectors are Linearly Independent or Dependent?
Linearly Independent Vectors: How to test the given vectors are linearly independent or not? The vectors v1,v2,v3,…vn in a vector space V are said to be linearly dependent if there exist constants c1,c2,c3,….cn not all zero such that: c1v1+c2v2+c3v3+……+cnvn=0 ————————-(i) Read More …
What is Linear combinations, Linear dependence and Linear Independence?
In this article you will get the idea of What is Linear combinations, Linear dependence and Linear Independence? Linear algebra is important for the turn of the mathematical branch. It is one of the main branches of math that can Read More …
What are the shortcuts for finding the determinant of a matrix?
Introduction In this article, I will discuss the shortcuts for finding the determinant of a matrix. Determinant has great significance in linear algebra. There are many practical problems that can be modeled as a linear system. When the systems are Read More …
Singular Value Decomposition with Eigen Value Equal to 0
Singular Value Decomposition Example