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September 23, 2025, 06:18:37 pm
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Author Topic: Finding the inverse of a 3x3 matrix  (Read 5875 times)  Share 

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Re: Finding the inverse of a 3x3 matrix
« Reply #15 on: November 24, 2010, 09:03:48 pm »
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The product of all eigenvalues is the determinant, right?
I just discovered this recently lol
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dcc

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Re: Finding the inverse of a 3x3 matrix
« Reply #16 on: November 24, 2010, 09:06:47 pm »
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Quote from: kamil9876 on November 24, 2010, 07:47:25 pm
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for invertible matrices without 0 as an eigenvalue

Does any invertible matrix have 0 as an eigenvalue? ;)

I'm a distinguished member of the accidental tautology club :D (perhaps they should call it the idiot club)
« Last Edit: November 24, 2010, 09:10:23 pm by dcc »
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kamil9876

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Re: Finding the inverse of a 3x3 matrix
« Reply #17 on: November 24, 2010, 09:07:21 pm »
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yes, though you have to count the "multiplicities". e.g:

2 0
0 2

has determinant 4=2*2, because the eigenvalue 2 appears "twice".
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

kamil9876

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Re: Finding the inverse of a 3x3 matrix
« Reply #18 on: November 24, 2010, 09:08:08 pm »
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Quote from: dcc on November 24, 2010, 09:06:47 pm
Quote from: kamil9876 on November 24, 2010, 07:47:25 pm
Quote
for invertible matrices without 0 as an eigenvalue

Does any invertible matrix have 0 as an eigenvalue? ;)

I'm a distinguished member of the accidental tautology club :D

Nice, I already knew that you either were or weren't.
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

dcc

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Re: Finding the inverse of a 3x3 matrix
« Reply #19 on: November 24, 2010, 09:12:20 pm »
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Exactly - a short summary is evaluating the characteristic polynomial at zero gives you (by definition) the determinant of the matrix.
« Last Edit: November 24, 2010, 09:16:51 pm by dcc »
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Tan

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Re: Finding the inverse of a 3x3 matrix
« Reply #20 on: November 28, 2010, 10:34:03 pm »
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Wow I didn't know finding the inverse of a 3x3 matrix was even possible. My own methods teacher said it can't be done lol.
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TrueTears

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Re: Finding the inverse of a 3x3 matrix
« Reply #21 on: November 29, 2010, 01:50:17 am »
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Quote from: Tan on November 28, 2010, 10:34:03 pm
Wow I didn't know finding the inverse of a 3x3 matrix was even possible. My own methods teacher said it can't be done lol.
lol he didn't want to scare you guys
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pi

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Re: Finding the inverse of a 3x3 matrix
« Reply #22 on: November 29, 2010, 01:46:16 pm »
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Quote from: TrueTears on November 29, 2010, 01:50:17 am
Quote from: Tan on November 28, 2010, 10:34:03 pm
Wow I didn't know finding the inverse of a 3x3 matrix was even possible. My own methods teacher said it can't be done lol.
lol he didn't want to scare you guys

too late ;)
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