An Introduction to Linear Algebra

This part is not so mine. But I do wish to put it here, so that It may be beneficial to somebody. This is only an introduction in layman language. This should encourage you to go on and take some books on this subject.

I wanna tell you here is not what my friend had to say in the DSP forum when he took a session. He did a good job only that what he talked was irrelevant to the audience. My idea as initiator of DSP forum in college and in here as well is to make DSP an perception, an intuitive feel rather than just mathematics. Mathematics is to substantiate what we talk and feel. It is the final step and not the first step in solving the problem, at least I wanna think so. That makes my life easier.

So, back to linear algebra.

Linear algebra, more specifically, vector spaces, I would like to think of it as only generalization of our usual understanding of algebra. That's all. Nothing more than that.

So, where do we start.

Lets talk about an N-dimensional euclidean space. Am i already going too fast. Well, By, "N-dimensional euclidean space" all that I mean is a Cartesian Co-ordinate system like system of x, y, ... co-ordinates, N such axises. Each axes is orthogonal to all others. "Orthogonal" just means normal or 90 degree. The generalisation is that the dimensions need not be like Cartesian. May be polar, a 2-dimensional euclidean space or extension of it as a cylindrical or spherical co-ordinate system.

I will not go into any formal definition of vector spaces, or for any other term that I would use. This is not the place for the formalities.

Then, having a space, we can visualise a point in this space, like in a 2-d plane. We can as well imagine lines or planes and volumes. If there are morfe than three dimensions we, call it a hyper object as in hyper-line.

This in essence an account of vector spaces in layman's language. We can extend most of the theorems in the regular school algebra with possibly a litle modification or some assumptins.