# 3.4 Basic complex and matrix operations

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This module covers basic complex and matrix operations in an m-file environment.

## Complex numbers

m-file environments have excellent support for complex numbers. The imaginaryunit is denoted by i or (as preferred in Electrical Engineering) j . To create complex variables ${z}_{1}=7+i$ and ${z}_{2}=2e^{(i\pi )}$ simply enter z1 = 7 + j and z2 = 2*exp(j*pi)

The table gives an overview of the basic functions for manipulating complex numbers, where $z$ is a complex number.

Manipulating complex numbers
m-file
Re( $z$ ) real(z)
Im( $z$ ) imag(z)
$\left|z\right|$ abs(z)
Angle( $z$ ) angle(z)
$z^{*}$ conj(z)

## Operations on matrices

In addition to scalars, m-file environments can operate on matrices. Some common matrix operations are shown in the Table below; in this table, M and N are matrices.

Common matrix operations
Operation m-file
$MN$ M*N
$M^{-1}$ inv(M)
$M^{T}$ M'
det( $M$ ) det(M)

Some useful facts:

• The functions length and size are used to find the dimensions of vectors and matrices, respectively.
• Operations can also be performed on each element of a vector or matrix by proceeding the operator by ".", e.g .* , .^ and ./ .

Let $A=\begin{pmatrix}1 & 1\\ 1 & 1\\ \end{pmatrix}$ . Then A^2 will return $\mathrm{AA}=\begin{pmatrix}2 & 2\\ 2 & 2\\ \end{pmatrix}$ , while A.^2 will return $\begin{pmatrix}1^{2} & 1^{2}\\ 1^{2} & 1^{2}\\ \end{pmatrix}=\begin{pmatrix}1 & 1\\ 1 & 1\\ \end{pmatrix}$ .

Given a vector x, compute a vector y having elements $y(n)=\frac{1}{\sin x(n)}$ . This can be easily be done the command y=1./sin(x) Note that using / in place of ./ would result in the (common) error " Matrix dimensions must agree ".

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what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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