What are Eigen Values and Eigen Vectors ?
In the most simplest words eigen values are set of scalars associated with an eigen vector of a matrix. But this definition might not give any sense so lets elaborate. So if we have a vector field and we apply a linear transformation to it then we notice there are few vectors, which remain pointing in same direction and they might be just scaled. So these vectors which don't change their direction are called eigen vectors and the factor by which they are scaled corresponds to their respective eigen value. The intuition and application of eigen vectors and eigen values are very important to scientists and engineers as it has several important applications besides an important mathematical tool to understand geometric transformation, its application in quantum mechanics is also significant. It's a very important tool for understanding fluids, and surprisingly it is also interestingly used in modern image processing software. Eigen values are apparently very simple to understand