Right, I have corrected it. :(FactChecker said:First, you have a mistake in the result for [2,3]. You need to correct that. Then take a general point, (x,y), in the ##R^2## plane and multiply it by the matrix. That will tell you where it ends up.
I agree with your statements.Poetria said:Right, I have corrected it. :(
You can look up the rotation matrix here:Poetria said:Homework Statement:: I have computed the matrix (it's ok):
##\begin{pmatrix}
0&1\\
-1&0\\
\end{pmatrix}##
The question is: what does this matrix do?
Relevant Equations:: To figure it out, I have sketched two vectors:
[2,3] and the other - after transformation: [3,-2]
I would say that what this matrix does is rotate e.g. a vector by ##\pi/2## clockwise. Am I right?
I would like to check my understanding.
PeroK said:You can look up the rotation matrix here:
https://en.wikipedia.org/wiki/Rotation_matrix
In your case, you are looking for ##\cos \theta = 0## and ##\sin \theta = -1##. This is satisfied by ##\theta = -\frac \pi 2##
A matrix function is a mathematical function that takes a matrix as its input and produces another matrix as its output. It can be thought of as a function that operates on matrices, similar to how regular functions operate on numbers.
A matrix function differs from a regular function in that it operates on matrices instead of individual numbers. This means that the input and output of a matrix function are both matrices, whereas a regular function takes in a single number and produces a single number as its output.
Some common examples of matrix functions include matrix addition, matrix multiplication, and matrix inversion. Other examples include functions like trace, determinant, and eigenvalues, which take in a matrix as their input and produce a single number as their output.
Matrix functions are essential in scientific research because they allow for the manipulation and analysis of data that is organized in a matrix format. Many scientific fields, such as physics, economics, and engineering, use matrix functions to model and solve complex problems.
Some tips for understanding matrix functions include familiarizing yourself with basic matrix operations, such as addition, multiplication, and inversion, as well as understanding the properties and rules that govern these operations. It is also helpful to practice using matrix functions in real-world applications to gain a better understanding of how they work.