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debjit625

Member

Registered: 2012-07-23

Posts: 101

Square of any determinant is symmetric.

This property is given in my book.
The square of any determinant is a symmetric determinant.
Well it works when I take a determinant say 3x3 and multiply it by itself using row to row multiplication.
But it fails if I multiply using row to column.

Thanks

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square of any determinant is symmetric.

Hi;

Can I see an example?

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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.

debjit625

Member

Registered: 2012-07-23

Posts: 101

Re: Square of any determinant is symmetric.

I asked this question on other fourms but I didnt got any answer
Here is a link please read it  https://www.physicsforums.com/threads/s … ic.873144/

Thanks

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square of any determinant is symmetric.

I am inclined to agree with fresh_42. A determinant is a scalar. It is one number.

For instance:

Symmetry in a number?

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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.

debjit625

Member

Registered: 2012-07-23

Posts: 101

Re: Square of any determinant is symmetric.

Well I too agree,but the problem is its not only in one book but rather more than one author is describing something like this.In that post I already gave some links to the books.

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square of any determinant is symmetric.

Matrices can be symmetric, determinants can not.

May I see your two calculations:

using row to row multiplication.But it fails if I multiply using row to column.

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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.

Alg Num Theory

Member

Registered: 2017-11-24

Posts: 693

Website

Re: Square of any determinant is symmetric.

Perhaps the book isn’t putting things very clearly. IMO what it’s trying to say is that the square of a determinant is the determinant of a symmetric matrix. For instance:

[list=*]
[*]

[/*]
[/list]

Last edited by Alg Num Theory (2017-11-24 22:05:15)

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Me, or the ugly man, whatever (3,3,6)