Book on matrices ??

HI All,
I am looking for a book on matrices with emphasis on enginnering
applications. I need insights into physical interpreations of  basic
matrix computaions as well as advanced matric methods like matrix
transformation, matrix decompositions etc, eigen analysis etc. A
intutive insight into enginnering applications of matrices is what I
am looking for (I know, I should have learnt it way back in undergard
school, but no one told me its gonna be this useful :( )

A search on amazon gave me hundreds of options and I do not have
access to any university libray .
Would appretiate refrals to books/papers/websites. Thanks In advance.
kal

This might help
http://archives.math.utk.edu/topics/linearAlgebra.html

Regards
Piyush

kpasad@hotmail.com (Kalpendu Pasad) wrote in message news:<8cd66b91.0407021628.4b17a078@posting.google.com>...
> HI All,
> I am looking for a book on matrices with emphasis on enginnering
> applications. I need insights into physical interpreations of  basic
> matrix computaions as well as advanced matric methods like matrix
> transformation, matrix decompositions etc, eigen analysis etc. A
> intutive insight into enginnering applications of matrices is what I
> am looking for (I know, I should have learnt it way back in undergard
> school, but no one told me its gonna be this useful :( )
> 
> A search on amazon gave me hundreds of options and I do not have
> access to any university libray .
> Would appretiate refrals to books/papers/websites. Thanks In advance.
> kal

the book by gilbert strang is a good one. He gives you a smooth ride
through linear algebra.

ashish

kpasad@hotmail.com (Kalpendu Pasad) wrote in message news:<8cd66b91.0407021628.4b17a078@posting.google.com>...
> HI All,
> I am looking for a book on matrices with emphasis on enginnering
> applications. I need insights into physical interpreations of  basic
> matrix computaions as well as advanced matric methods like matrix
> transformation, matrix decompositions etc, eigen analysis etc. A
> intutive insight into enginnering applications of matrices is what I
> am looking for (I know, I should have learnt it way back in undergard
> school, but no one told me its gonna be this useful :( )

Waddayaknow!! Who would have known that those sadistic mo******ckers
who teach at college and university do that because what they teach 
is *useful* and not just for their own twisted pleasures...

[Yep. I have done some teaching at university and, yep, I do tend to get 
a bit curse when somebody asks what the use is for anything I might 
present in class.]

> A search on amazon gave me hundreds of options and I do not have
> access to any university libray .
> Would appretiate refrals to books/papers/websites. Thanks In advance.
> kal

If I were to recomend one book on linear algebra, it would be 

Golub & van Loan: Matrix Computations, 3rd ed.
         John Hopkins, 1996.

It's not very easy to read if you know no linear algebra in advance, 
but if your interest is serious, you can't avoid it. 

A good starting text would be 

Strang: Linear Algebra and its Applications
        1988.

This book lets you know what's going on and the general philosophy 
of linear algebra, but I don't find it to be very good on algorithms 
and applications.

For some general applications of maths and linear algebra, try 

Strang: Introduction to applied Mathemathics
        Wellesley Cambridge Press, 1986

Rune

The matter of fact seems to be that matrices are mathematical tools,
and using advanced matrix operations is akin to using complex numbers.
You loose the “physical interpretation” and tend to drift
into a sea of pure mathematics. Some concepts like linear
transformations do translate to the physical world. But I
haven’t been able to get “feel” for other useful
concepts aka eigen analysis, decompositions et al.
Golub and van loan, I did refer. But found it difficult, maybe afert
some more preliminary stuff. Strangs book seems to be a referred
multiple time, will check it out. Other recommendations would be
definitely helpful.
Thanks!
Kalpendu

allnor@tele.ntnu.no (Rune Allnor) wrote in message news:<f56893ae.0407040203.167cb121@posting.google.com>...
> kpasad@hotmail.com (Kalpendu Pasad) wrote in message news:<8cd66b91.0407021628.4b17a078@posting.google.com>...
> > HI All,
> > I am looking for a book on matrices with emphasis on enginnering
> > applications. I need insights into physical interpreations of  basic
> > matrix computaions as well as advanced matric methods like matrix
> > transformation, matrix decompositions etc, eigen analysis etc. A
> > intutive insight into enginnering applications of matrices is what I
> > am looking for (I know, I should have learnt it way back in undergard
> > school, but no one told me its gonna be this useful :( )
> 
> Waddayaknow!! Who would have known that those sadistic mo******ckers
> who teach at college and university do that because what they teach 
> is *useful* and not just for their own twisted pleasures...
> 
> [Yep. I have done some teaching at university and, yep, I do tend to get 
> a bit curse when somebody asks what the use is for anything I might 
> present in class.]
> 
> > A search on amazon gave me hundreds of options and I do not have
> > access to any university libray .
> > Would appretiate refrals to books/papers/websites. Thanks In advance.
> > kal
> 
> If I were to recomend one book on linear algebra, it would be 
> 
> Golub & van Loan: Matrix Computations, 3rd ed.
>          John Hopkins, 1996.
> 
> It's not very easy to read if you know no linear algebra in advance, 
> but if your interest is serious, you can't avoid it. 
> 
> A good starting text would be 
> 
> Strang: Linear Algebra and its Applications
>         1988.
> 
> This book lets you know what's going on and the general philosophy 
> of linear algebra, but I don't find it to be very good on algorithms 
> and applications.
> 
> For some general applications of maths and linear algebra, try 
> 
> Strang: Introduction to applied Mathemathics
>         Wellesley Cambridge Press, 1986
> 
> Rune

kpasad@hotmail.com (Kalpendu Pasad) wrote in message news:<8cd66b91.0407051124.57a1a6c2@posting.google.com>...
> The matter of fact seems to be that matrices are mathematical tools,
> and using advanced matrix operations is akin to using complex numbers.
> You loose the &#8220;physical interpretation&#8221; and tend to drift
> into a sea of pure mathematics. Some concepts like linear
> transformations do translate to the physical world. But I
> haven&#8217;t been able to get &#8220;feel&#8221; for other useful
> concepts aka eigen analysis, decompositions et al.

That's a very good summary of the whole subject of linear algebra.

Some concepts are abstract and belong to the "purely mathematical"
world. I have, for instance, after having used linear algebra almost 
every day for ten years never been able to grasp what a determinant
is. Other concepts, like vector spaces (Strang's book is a brilliant 
introduction to vector spaces) are so "real" to me that manifolds in 
26-dimensional complex-valued subspaces almost are tangible. Still 
other concepts are purely algorithms, methods and procedures to 
obtain some sort of result with a minimum amount of fuzz, or where 
some particular aspect of the matrix one works on is exploited.

There was a time when I strove for "physical" interpretations of 
various aspects of linear algebra. I really didn't succeed that much;
the big hurdle (and to me most useful result) was to develop an 
intution regarding vector spaces. Everything else then reduces to 
vectors with particular properties in a given vector space, or methods 
to manipulate such vectors in whatever vector space. 

Try and get the Strang book, and reat the first two or three chapters 
there. I can think of no better introduction to these concepts.

Rune

Rune Allnor wrote:

> Some concepts are abstract and belong to the "purely mathematical"
> world. I have, for instance, after having used linear algebra almost 
> every day for ten years never been able to grasp what a determinant
> is. 

God, I'm glad to hear you say that.  All I know about them 
is that you divide the cofactor array by it to give you the 
inverse and that it goes away if the matrix is linearly 
dependant.  That operational understanding amounts to 
absolutely nothing, really, at all.

> Other concepts, like vector spaces (Strang's book is a brilliant 
> introduction to vector spaces) are so "real" to me that manifolds in 
> 26-dimensional complex-valued subspaces almost are tangible. 

I'm sold.  On order.


Thanks,

Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

> Rune Allnor wrote:
> 
> > Some concepts are abstract and belong to the "purely mathematical"
> > world. I have, for instance, after having used linear algebra almost
> > every day for ten years never been able to grasp what a determinant
> > is.

Ratio of volumes in the two spaces
-- 
Ron Hardin
rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.

Ron Hardin wrote:
> > Rune Allnor wrote:
> > 
> > > Some concepts are abstract and belong to the "purely mathematical"
> > > world. I have, for instance, after having used linear algebra almost
> > > every day for ten years never been able to grasp what a determinant
> > > is.
> 
> Ratio of volumes in the two spaces

Which two spaces?

Ron Hardin <rhhardin@mindspring.com> wrote in message news:<40EA6C6E.724A@mindspring.com>...
> > Rune Allnor wrote:
> > 
> > > Some concepts are abstract and belong to the "purely mathematical"
> > > world. I have, for instance, after having used linear algebra almost
> > > every day for ten years never been able to grasp what a determinant
> > > is.
> 
> Ratio of volumes in the two spaces

Well, yes, I have seen that being mentioned here and there. The problem 
is, I don't understand why this is what the determinant expresses. Which 
probably means I haven't spent enough time contemplating the determinant. 
Which I see no reason to do. And even so, accepting this interpretation 
requires the vector space concept and basis shift transforms etc to be 
in place beforehand. Which it wasn't when I last read about determinants.

When I took the first maths course that included linear algebra, I just 
didn't get it. These determinants took up some 50% or more of the time 
spent on linear algebra. Cofactors. Minors. Cramer's rule. Some matrix 
inversion. Lots of algebraic drudgery, no explanation of concepts and 
a very unforgiving exam. There were 10 questions on the exam, labeled 
a) to j). All the questions were interconnected, so getting any 
particular question right, required everything being right in all 
prior questions. I made a blunder in question c) and knew it, but had 
no time to find, let alone correct, the algebraic blunder. Imagine my 
motivation for answering the remaining 7 questions... Somehow I got 
through. Instead of going on with the wrong answers, I explained how I 
would have used the previous answers in each question but did no actual 
computations. The grade on that exam turned out, to my astonishment, 
almost decent.

Anyway, the following year a friend of mine took the same course. 
I couldn't really understand that he took the same course as me; 
that only the teacher had been changed. My friend was very excited 
about all these fancy projections, basis transforms and what not. 
So I got curious. All this happened when I was at the college of 
engineering. When I came to university they gave an optional maths 
course, dedicated completely to linear algebra, that was based on 
the Strang book. I jumped on, got very confused and got my worst 
maths grade ever. Nevertheless, after getting more involved with 
advanced DSP I started seeing the usefulness of linear algebra. 
The problem was that all I found useful, like vector spaces, basis 
shifts, eigenanalysis, SVDs, etc, was what I learned in the optional 
course. Basically the only thing left from the first introduction 
course, was that matrix notation uses boldface letters. No determinants 
any more. I had to look up "Cramer's rule" when I stumbled across the 
term a few months ago. And with EISPACK/LINPACK/LAPACK (not to 
mention Matlab) available, who have heard of cofactors and minors 
for the last 25 years?

I guess my point is that linear algebra, as presented in maths intro
courses, has little to do with that powerful analyis tool I find
so immensely useful. Which, I guess, is a pity.

Rune