Linear transformation

by matqkks
Tags: linear, linear algebra, transformations, vector spaces
matqkks is offline
Feb13-12, 05:17 AM
P: 150
Why would you want to use a matrix for a linear transformation?
Why not just use the given transformation instead of writing it as a matrix?
Phys.Org News Partner Science news on
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
HallsofIvy is offline
Feb13-12, 03:48 PM
Sci Advisor
PF Gold
P: 38,902
If you have a number of rotations to be performed in succession, you can just multiply the matrices. Also you can determine information about a rotation, for example the axis of rotation, by calclulating the eigevectors of the matrix.
micromass is offline
Feb13-12, 04:28 PM
micromass's Avatar
P: 16,703
Using the transformation or using the matrix is equivalent. You won't lose information if you use the matrix.

If you want to keep on using the transformation, then you can do this. But in many cases, using the matrix is simply much easier. Finding eigenvalues for example is much easier with a matrix than with a transformation.

Deveno is offline
Feb15-12, 01:01 PM
Sci Advisor
P: 906

Linear transformation

one reason is:

a matrix calculation reduces the computation of composition of linear transformations, as well as the computation of image elements under a linear transformation, to arithmatic operations in the underlying field. that is:


sometimes, this is preferrable for getting "actual answers" in a physical application, where some preferred basis (coordinate system) might already be supplied.

for example, the differentiation operator is a linear transformation from Pn(F) to Pn(F).

actually "computing a derivative" IS just computing the matrix product [D]B[p]B = [p']B:

for n = 2, and F = R, we have for the basis B = {1,x,x2}, that [D]B=

[0 1 0]
[0 0 2]
[0 0 0],

or that if p(x) = a + bx + cx2,

p'(x) = b + 2cx.

of course, this would be just as easy using D(p) = p' using the calculus definition,

but it's not so clear what happens if you want to use THIS basis: {1+x,1-x,1-x2}, using the calculus definition, whereas the matrix form makes it transparent.
matqkks is offline
Feb18-12, 11:06 AM
P: 150
Is it by using a matrix representation of a derivative that CAS and programmable calculators evaluate derivatives?

Register to reply

Related Discussions
Linear transformation and matrix transformation Linear & Abstract Algebra 5
A couple linear algebra questions (basis and linear transformation Calculus & Beyond Homework 5
[SOLVED] linear algebra - inner product and linear transformation question Calculus & Beyond Homework 0
Linear Algebra: Linear Transformation and Linear Independence Calculus & Beyond Homework 8
LINEAR ALGEBRA - Describe the kernel of a linear transformation GEOMETRICALLY Calculus & Beyond Homework 6