books on linear algebra

Question

What are some books that focus on the more intuitive part of linear algebra study?
So far only this series of lessons have been satisfactory, but they are very consice, and the books that I have come across so far focus on a more rigorous definition of linear algebra that start with solving equations. Where and how could I get a more geometrically interpretable study for linear algebra?

Answer 1

1. Linear Algebra: A Geometric Approach by S. Kumaresan

   This clear, concise and highly readable text is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focusses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions. From the very start, linear algebra is presented as an extension of the theory of simultaneous linear equations and their geometric interpretation is shown to be a recurring theme of the subject.

2. Linear Algebra Through Geometry by T. Banchoff

   Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms.

Answer 2

You may follow lectures by Prof. Gilbert Strang (MIT) and his books. He is a legend.

Answer 3

This is the book I was introduced to linear algebra by:

"Linear Algebra with Applications" By Keith Nicholson.

It does a good job of geometrically explaining mappings, eigenvalues, vector geometry, and some introductory complex arithmetic material.