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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

general 4x4 determinant

Given the following
4x4 matrix:

Is this a correct
equation for the
determinant?

Since I haven't learned to read
some math topics correctly, the above equation
I built by guessing may be correct or false.
So I am asking because I cannot decifer
the wikipedia nxn paragraph, but I think
I might have the right idea.

Last edited by John E. Franklin (2014-02-24 04:04:36)

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: general 4x4 determinant

Hi;

I am not getting that. For training , it might be better to work with numbers.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: general 4x4 determinant

hi John,

That's one to make my eyes screwy.  eek!

But I think there are three sign errors:

cf(lm-ip)
de(jo-kn)
dg(in-jm)

If you look at your brackets each one occurs twice, once with the terms reversed.
In those three the terms are not reversed.

If I had to do one of these, I'd write +a, then -b then +c then -d multiplied by the corresponding 3 by 3.  Then do each 3 by 3 in terms of 2 by 2s and so on.

Bob

LATER EDIT I think two more:  be(kp-lo) and ch(in-jm)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: general 4x4 determinant

I watched some videos so I think I got it right now!

Last edited by John E. Franklin (2014-02-24 07:22:10)

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: general 4x4 determinant

Last edited by John E. Franklin (2014-02-24 07:16:55)

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igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: general 4x4 determinant

So far so good. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc.

Guest

Re: general 4x4 determinant

As a 'check', in general the determinant of an n x n matrix will require summing n! terms, each of which is a product of n terms.

There is an explicit formula for the determinant of an n x n matrix, called the Leibniz formula, which involves the sum of a product of permutations.

zetafunc.

Guest

Re: general 4x4 determinant

There are tricks that we sometimes use when calculating determinants -- for instance, if the matrix is triangular, then the determinant is simply the product of the entries along the main diagonal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: general 4x4 determinant

sweet zeta;
  I'm watching some great lectures from MIT in 2005 on Linear Algebra.
Here's the youtube title:
Lec 1 MIT 18.06 Linear Algebra, Spring 2005
Lec 2 ...
Lec 3 ...
The insight of the professor is astounding compared to what I didn't learn in college
because my professor was drunk and then they fired him soon thereafter.

Last edited by John E. Franklin (2014-02-25 02:16:56)

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igloo myrtilles fourmis

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: general 4x4 determinant

Hi John E. Franklin;

Did you finish the lectures?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: general 4x4 determinant

nope.  got interrupted when switched devices.  thanks 4 reminding me...

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igloo myrtilles fourmis

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: general 4x4 determinant

They really are nice lectures. I think they were the ones from which I first learned linear algebra.