It's been a long time since I studied Math and, going over my old notes, I
have a question:

I found a section where my instructor took J, multiplied it by an
orthonormal matrix and it's inverse, producing some matrix A, which he then

If you follow me: In the notes my instructor denotes the orthonormal
matrix as P. So I'm a bit confused as to why I'm constructing A (It appears

1) Why denote this seemingly random orthonormal matrix as P only to turn
around and recalculate P?

Could anyone shed some light on this?

Much Thanks!

"kroenecker" <mojowings@hotmail.com> wrote in message
news:3978359.1165639204130.JavaMail.jakarta@nitrogen.mathforum.org...
It's been a long time since I studied Math and, going over my old notes,
I
have a question:

I found a section where my instructor took J, multiplied it by an
orthonormal matrix and it's inverse, producing some matrix A, which he
then
used to find the matrix P in A = PJP(-1).

well A = PJP(-1) is unsurprisingly called a jordan decomposition, and its
common to find it by firstly finding P (which is called a canonical basis)
using filipov's algorithm. J can then be found from J = P(-1)AP

where did your instructor pluck the initial J from? maybe he was just
trying to demonstrate what a jordan decomposition was before trying to
show
you how to find one.

If you follow me: In the notes my instructor denotes the orthonormal
matrix as P. So I'm a bit confused as to why I'm constructing A (It
appears
that I can use any orthonormal matrix) only to turn around and construct
P.

1) Why denote this seemingly random orthonormal matrix as P only to turn
around and recalculate P?

Could anyone shed some light on this?

Much Thanks!

Well I have to admit that it was a couple of years ago when I took the
class so I don't exactly remember.

The order was:

Given J:

1) Solve OJO(-1) where O is an orthogonal matrix.

2) Then take the resulting matrix, A, and solve for independent
eigenvalues in order to construct P.

3) Finally, show that A does in fact = PJP(-1)

Does doing things in that order make much sense? I wonder what he was
trying to show? I took a couple of different orthogonal matrices and found

As a side note what is Filipov's Algorithm? I suppose I should probably
look on wikipedia

"kroenecker" <mojowings@hotmail.com> wrote in message
news:14641099.1165720603106.JavaMail.jakarta@nitrogen.mathforum.org...
Well I have to admit that it was a couple of years ago when I took the
class so I don't exactly remember.

The order was:

Given J:

1) Solve OJO(-1) where O is an orthogonal matrix.

when you say solve here what do you mean exactly? I presume J is known,
so
you mean you then have a completely unknown O that you need to find?
i know that the jordan decomposition is often associated with the matrix
equation AX = XB, so did you start with a similar equation at all?


2) Then take the resulting matrix, A, and solve for independent
eigenvalues in order to construct P.

3) Finally, show that A does in fact = PJP(-1)

Does doing things in that order make much sense? I wonder what he was
trying to show? I took a couple of different orthogonal matrices and
found
that they would produce different A matrices so I'm a bit lost as to what
he
was showing.

i cant say i've seen producing a jordan decomposition in this way before,
as
that is what seems that your lecturer is showing. you usually find P first
before using that to find J.


As a side note what is Filipov's Algorithm? I suppose I should probably
look on wikipedia :)

try this

http://www.cs.ut.ee/~toomas_l/linalg/lin2/node21.html#SECTION000153000000000
00000

Well I have to admit that it was a couple of years ago when I took the class so I don't exactly remember.

The order was:

Given J:

1) Solve OJO(-1) where O is an orthogonal matrix.

2) Then take the resulting matrix, A, and solve for independent eigenvalues in order to construct P.

3) Finally, show that A does in fact = PJP(-1)

Does doing things in that order make much sense? I wonder what he was trying to show? I took a couple of different orthogonal matrices and found that they would produce different A matrices so I'm a bit lost as to what he was showing.

As a side note what is Filipov's Algorithm? I suppose I should probably look on wikipedia