3. A LITTLE BIT OF HISTORY
The history of matrices goes back to
ancient times , but the term
“Matrix” was not applied to the
concept till 1850
Matrix is the Latin word for womb
and it retains that sense in English
It can also mean more generally any
place where something is formed or
produced
A LITTLE BIT OF HISTORY
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4. A LITTLE BIT OF HISTORY
He was instrumental in proposing a
matrix concept independent of equation
systems. In 1858 Cayley published
his A memoir on the theory of matrices
which he proposed and demonstrated
the Cayley-Hamilton theorem .
In linear algebra, the Cayley–Hamilton
theorem states that every square
matrix over a commutative ring satisfies
its own characteristic equation.
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6. Use of Matrices In Computer Graphics
APPLICATION
Earlier architecture, cartoons, automation
were done by hand drawings but nowadays
they are done by using computer graphics.
Square matrices very easily represent linear
transformation of objects. In Graphics, digital
image is treated as a matrix to start with
Matrixoperations such as translation, rotation
and sealing are used in graphics. For
transformation of a point we use the equation
EXAMPLE :
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7. Use of Matrices in Cryptography
Cryptography is the technique to encrypt data
so that only the relevant person can get the
data and relate information.
One type of code, which is extremely difficult
to break, makes use of a large matrix to
encode a message.
The receiver of the message decodes it using
the inverse of the matrix.
This first matrix, used by the sender is called the
encoding matrix and its inverse is called the
decoding matrix, which is used by the receiver.
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8. A LITTLE BIT OF HISTORY
Use of Matrices in Wireless
ommunication Matrices are used to model
the wireless signals and to optimize them.
Matrices help in processing and representing
digital images.
important part of the telecommunication
industry. Sensor array signal processing
focuses on signal enumeration and source
location applications and presents a huge
importance in many domains such as radar
signals and underwater surveillance.
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9. Use of Matrices in Robotics
In robotics and automation, matrices are
the base elements for the robot
movements
The movements of the robots are
programmed in MATLAB using matrix pencil
method.
Matrices are used for movements in Robot
Arms. ROBOTICS
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10. Use of Matrices in Chemical
In chemistry we use matrix methodology
to balance the chemical equations
Initially we transform the chemical equations
into the matrices form.
Then we apply Gauss Jordon method to
calculate the chemical reactions
aFeCl2 + bNa3(PO4) cFe3(PO4)2 + dNaCl
Fe: (1×a) + (0×b) –(3×c) = 0×d
Cl: (2 × a)+(0×b )+(0 × c) = 1 × d
Na: (0 × a)+(3 × b)+(0× c) = 1 × d
(PO4): (0×a)+(1×b)–(2 × c) = 0 × d
EX:
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