MatLab | Basic Knowledge

Arrays and Metrices:

• Variable for one dimensional vector should be start with lowercase.
• Variable for two dimensional vector (matrix) should be start with Uppercase.
• Scalars is  one by one matrices. 
• Not like java or ruby, the first element of an array in Matlab is indexed by number 1
• Let say x is a 3x3 matrix. X(2,2) return the element from second row and second column. If you want to change the value, simply assign a new value. X(2,2) = 5
• If a variable XYZ doesn't exist and you type in a command XYZ(2,2) = 3 Matlab will give you 2x2 matrix with XYZ(2,2) equals to 3 and rest elements of 0
• X(2,[1 3]) gives you the 1st and the 3rd elements of the second row of a matrix.
• X([1 2],2) gives you the 1st and the 2nd elements of the second column of a matrix.
• For matrix multiplication the inner dimension muss be equal. 5x3 matrix * 3x4 matrix works just fine. but 5x3 matrix * 2x4 matrix gives you an error.
• Use randi( maxNumber , numberOfRow , numberOfColumn) to create a random matrix of integers
• let say X is a matrix. X^2 means X*X or matrix multiplication. and X.^2 means to square each element of X. And X.^Y means to tell Matlab to exponentiate each element of X to the power of element of Y of the same index. 
• Use find(A); to find all non zero elements of matrix A. The output of this function is a vector containing linear indices of each non zero elements in matrix A



Elements with index: 1, 3, 5 and 7 are not zero

Operators:  

• Colon ':' operator: x = 1 : 3 : 7 means we tell Matlab to create row vector start from 1 increment it by 3 till its maximum of 7. it will give you a result x = 1 4 7
• Colon operator is very useful to create an array of odd or even numbers 1:2:7 will return an array of odd numbers[1, 3, 5, 7]
• Colon operator can also give you an array in a decreasing order. 10:-3:1 will return [10, 7, 4, 1]
• ints = 1 : 10 means give me an array of numbers from one to ten
• A * B or mtimes(A,B)means matrix A times matrix B. A .* B or times(A,B)
More operator can be found in Matlab Operators

• size(variable) gives you the size of a matrix. e.g. x = [3 2 4 ; 2 5 6] and size(x) gives you ans = 2 3 matrix of 2 rows and 3 columns 
• Any scalar for. e.g. x = 2 and size(x) gives you ans = 1 1 since in Matlab scalar is one by one matrix.
• Some operators can also be written as a function: plus(1,2) means 1+2 ans = 3and colon(1,7) gives you [1, 2, 3, 4, 5, 6, 7]

Function handles

Function handles are Variables that allow you to invoke a function indirectly. Using function handles you can pass a function as a parameter of another function. For example I have a function f(x)=3x^4 - 2x^2

And we want to pass this function to another function like this:

Now if you try to call the function using diffQuotF(f, x0, h) you'll get an error message.

The right way to pass the ' f ' function as a parameter is by using the @ (at) sign before the ' f '. like this: