Vectors and Matrices

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Vectors and Matrices

• In MATLAB a vector can be defined as row vector
  or as a column vector.
• A vector of length n can be visualized as matrix
  of size 1xn or nx1.

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Vectors and Matrices

• Matrices can be of different sizes, either square
  matrices of size NxN or rectangular NxM.
• Note that vectors are special case of matrices.

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Some Special Vectors and Matrices
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Matrix Calculations

• Addition
• Multiplication
• Inverse

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Solving Simultaneous EquationsAxb

• Amatrix of coefficients,
• x vector of variables,
• b vector of values.
• In matrix form the above system and its solution
  can be written as
• In MATLAB we write as x inv(A)b

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Loops

• Two different types of loops exist in MATLAB.
• for and
• while
• Their structure is as shown here

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for loop

• A simple for loop to calculate and display
  squares of numbers from 1 to 5.

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for loop (contd.)

• We can write the same for loop with some change.
  Now we are saving the results in a vector named
  result.

Note that the squared values will be saved in the
result vector. The vector must be initialized
before assigning any value to it. Note that this
is the case for vectors and matrices only. We
dont need to initialize scalars in MATLAB.
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for loop (contd.)

• The control index of the for loop shown in the
  previous slides was incremented by 1. We can
  increment the control index by any arbitrary
  value as required.
• In the following example odd numbers from 1 to 9
  are printed.

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while loop

• While loop continue to execute if the given
  condition is true.
• A condition is true if it is not equal to 0.
• A simple while loop to display numbers from 1 to
  10 is shown here.

In this while loop at each iteration the value
of i is incremented after the value is
printed.
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Logical Operators

• AND, OR, and INVERT logical operations can be
  performed in MATLAB.
• The symbols used for these operators are ,
  , and respectively for AND, OR, and
  INVERT.
• A logical operation always results in a 1 or
  0.

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Some more logical operators

• Other logical operators in MATLAB include
• Note that the results of these operations are
  also either 1 or 0.

lt Less than
gt Greater than
Equal to
lt Less than or equal to
gt Greater than or equal to
Not equal to
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Examples logical operations

• Lets say, a1, b2, and c1. Then,
• Altb results in TRUE I.e. 1
• Agtb results in FALSE I.e. 0
• Ab results in FALSE I.e. 0
• Ac results in TRUE I.e. 1
• Ac altb results in 1.
• Several examples can be used to show the usage of
  these operators.

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while loop revisited

• Now we can show the usage of these logical
  operations in the while loop as condition.
• Say a1, then the following code results in the
  execution of loop until the condition altb gets
  FALSE.

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if statement

• if statement checks whether the condition given
  to it is TRUE or FALSE.
• If the condition evaluates to TRUE the
  ltstatementsgt are executed otherwise not.
• Unlike the for and while loops the ltstatementsgt
  inside the if statement are executed only once.

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if-else statement

• If-else is used if we want to perform two
  different tasks depending upon the condition is
  TRUE or FALSE.

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We wish to use if and else statement to
decide upon if the input integer is an odd or an
even number. The Matlab code for the purpose is
shown below
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Functions in Matlab

• Functions are actually computer
  routines(programs) to perform specific task.
• Matlab is rich in built-in function
• A function is called, user gives specific
  input(s) to the function, which generates the
  required output(s).

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Example of built-in functions

• Our objective is to calculate mean or average of
  certain vector x.
• We call the built in function mean of Matlab
  and give x as an input to the function.
• The mean is calculated and is stored in variable
  y.

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• We can also built our own functions and call them
  when required.
• The functions are the m-files.
• For example for a given quadratic equation we
  wish to calculate the roots of equation. So we
  build our own function call and use the
  quadratic formula to solve for x1 and x2.

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• In our main program the function is called and
  the inputs a, b and c are given to the
  function which calculates the required roots

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Plotting in Matlab

• Matlab uses plot command to plot the curves
  with different line style and colors
• Example follows

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• Thank You