10657
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Determinant Using Traces
The determinant of a square matrix can be computed as a polynomial of traces of the matrix and its powers. This expression greatly simplifies for traceless matrices.
Contributed by:
Oleksandr Pavlyk
SNAPSHOTS
DETAILS
Consider the polynomial
in
of degree
, where
is the
identity matrix. Its leading coefficient is
.
On the other hand,
.
Comparing coefficients in the powers of λ gives
.
This derivation is due to Vladimir Dudchenko, the first prize winner of the
Russian Student
Mathematica
Contest
.
RELATED LINKS
Determinant
(
Wolfram
MathWorld
)
Matrix Trace
(
Wolfram
MathWorld
)
Our First Russian Student Competition
(
Wolfram Blog
)
PERMANENT CITATION
"
The Determinant Using Traces
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheDeterminantUsingTraces/
Contributed by:
Oleksandr Pavlyk
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Graph of Inequalities
Ed Pegg Jr
2D Vector Addition
Joe Bolte
Euler Angles for Space Shuttle
S. M. Blinder
From Vector to Plane
Ed Pegg Jr
A Simple, Standard Linear Programming Scenario
Chris Boucher
QR Decomposition
Chris Boucher
Gram-Schmidt Process in Two Dimensions
Chris Boucher
3x3 Matrix Explorer
Chris Boucher
Eigenvectors in 2D
David K. Watson
Affine Transform
Bernard Vuilleumier
Related Topics
College Mathematics
Linear Algebra
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+