Register to reply

Transposition of a matrix

by matqkks
Tags: linear alegbra, matrices, transpose
Share this thread:
Jul21-11, 06:04 AM
P: 153
Why is the transpose of a matrix important?
To find the inverse by cofactors we need the transpose but I would never find the inverse of a matrix by using cofactors.
Phys.Org News Partner Science news on
An interesting glimpse into how future state-of-the-art electronics might work
Tissue regeneration using anti-inflammatory nanomolecules
C2D2 fighting corrosion
Jul21-11, 06:16 AM
Sci Advisor
PF Gold
Fredrik's Avatar
P: 9,356
I think the main reason why the transpose is useful is that the standard inner product on the vector space of n1 matrices is [itex]\langle x,y\rangle=x^Ty[/itex]. This implies that a rotation R must satisfy [itex]R^TR=I[/itex].

I think that cofactor stuff is sometimes useful in proofs, but you're right that if you just want to find the inverse of a given matrix, there are better ways to do it.
Jul21-11, 08:45 AM
P: 34
There are of course many ways to invert a matrix but thie is not the only use for the transpose.

Systems of linear equations can be reformulated into matrix systems by looking at the equation xAx^{T} = b where x is a n x 1 column vector with entries {x_{1},...,x_{n}} and Z is a square matrix n x n with entries (for real valued equations, say) in /mathbb{R}. The matrix b is then also an $n x 1$ column matrix of numbers in /mathbb{R} too.

Register to reply

Related Discussions
Using MPI to perform the Matrix Transposition Engineering, Comp Sci, & Technology Homework 0
T = sqrt(m/k)^(1/2pi), solve for k Precalculus Mathematics Homework 8
Transposition invariance General Physics 0
Simple transposition Biology, Chemistry & Other Homework 1
Solve 2x + y + y' x = 3y^2 y', why is this wrong? Precalculus Mathematics Homework 4