Tasting Linear Algebra

The mathematical definition of vector

Matrices and Linear Algebra (an exposition for secondary school students and laymen)

Einstein summation convention

The identity matrix

The Kronecker delta symbol

Row reduction and echelon form

Linear independence, linear dependence and basis

Change of basis

 

Comments

Linear algebra and calculus are the languages of quantum mechanics. In this section, we give you what the rough idea of linear algebra is like to motivate you to study linear algebra and quantum mechanics in our later sections on them. Some high school students study a little bit of matrices, but I dont think that they can appreciate the real value of matrices until they learn linear algebra, usually in the second semester of their college freshman year. Matrices and Linear Algebra is written so that readers can appreciate the real value of matrices.