Fastest way to find inverse of 4x4 matrix?

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    Inverse Matrix
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Homework Help Overview

The discussion revolves around finding the fastest method to compute the inverse of a 4x4 matrix, a topic within linear algebra.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss various methods for finding the inverse, including row reduction and the use of determinants and adjugate matrices. There is a debate about the efficiency of these methods, with some questioning the practicality of calculating determinants for larger matrices.

Discussion Status

The conversation is ongoing, with participants sharing their experiences and preferences regarding different methods. Some express skepticism about the efficiency of using determinants, while others advocate for row reduction as a potentially faster approach.

Contextual Notes

Participants note the challenges associated with calculating determinants, including the computational effort and potential for roundoff errors. There is an acknowledgment of the varying effectiveness of methods depending on specific circumstances.

pyroknife
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What is the fastest way to find the inverse of a 4x4 matrix?

The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.
 
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pyroknife said:
What is the fastest way to find the inverse of a 4x4 matrix?

The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.

It is often (but not always) faster to use the determinant and the adjugate matrix.
 
gabbagabbahey said:
It is often (but not always) faster to use the determinant and the adjugate matrix.

It is hardly ever faster to use determinants. You would need to calculate 16 determinants, each of which is 3x3, so each involves 9 three-factor multiplications, plus keeping track of signs and worrying about roundoff error effects. Direct row-reduction is likely much faster in the vast majority of cases. And, yes, it can involve a lot of work, but that's life!

RGV
 
Personally, I've always felt that row-reducing was faster than finding the determinant.
 

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