Product of multiple determinants

Click For Summary
SUMMARY

The discussion focuses on calculating the product of the determinants of multiple 2x2 matrices, specifically the expression \(\Pi|A_s|^{-1/2}\) for matrices \(A_s\) indexed from 1 to 50. A sample matrix formula is provided: \(A_s=\left(\begin{array}{cc}(-1)^s&\frac{s}{s+1}\\s^2-1&1\end{array}\right)\). Participants are encouraged to share methods for generating these matrices or to provide existing data for computational purposes. The goal is to simplify the calculation process and explore potential formulas.

PREREQUISITES
  • Understanding of linear algebra, specifically matrix determinants.
  • Familiarity with 2x2 matrix operations.
  • Basic knowledge of mathematical notation and expressions.
  • Experience with computational tools for matrix calculations, such as Python or MATLAB.
NEXT STEPS
  • Research methods for calculating determinants of 2x2 matrices efficiently.
  • Explore Python libraries such as NumPy for matrix operations and determinant calculations.
  • Learn about symbolic computation tools like SymPy for generating and manipulating matrix formulas.
  • Investigate optimization techniques for handling large sets of matrices in computational tasks.
USEFUL FOR

Mathematicians, data scientists, and engineers who work with linear algebra and matrix computations, particularly those interested in optimizing determinant calculations for multiple matrices.

brokephd
Messages
1
Reaction score
0
Hello,

I have several 2x2 matrices, A_s, indexed from s=1 to 50. I need to take the product of their determinants raised to the -1/2 power, i.e.,

[tex]\Pi[/tex]|A_s|[tex]^{-1/2}[/tex]

Can this problem be simplified any further?
 
Physics news on Phys.org
These matrices, do you have a formula for them? Such as, (I made this up, not from this problem): [tex]A_s=\left(\begin{array}{cc}(-1)^s&\frac{s}{s+1}\\s^2-1&1\end{array}\right)[/tex]. In this case, give the formula (or some other procedure for generating them) and we'll see.

Or perhaps you have these matrices written out, or stored as a data? In this case, I would use a computer to do the calculation.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
4
Views
1K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K