Reverse Polish Notation & Polish Notation

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Reverse Polish Notation



-> Take e = a – b ÷ ( c + d )
-> Lets convert it into Reverse Polish Notation
-> ( c + d ) will be cd+ and Let p = cd+
-> e = a – b ÷ p
-> b ÷ p will be bp÷ and Let q = bp÷
-> e = a – q
-> a – q will be aq- and Let r = aq-
-> e = r
-> e = r will be er= and let s = er=
-> s

-> Lets put the values back
-> s will be er=
-> er= will be eaq-=
-> eaq-= will be eabp÷-=
-> eabp÷-= will be eabcd+÷-=
-> eabcd+÷-=

Polish Notation



-> Take e = a – b ÷ ( c + d )
-> Lets convert it into Polish Notation
-> ( c + d ) will be +cd and Let p = +cd
-> e = a – b ÷ p
-> b ÷ p will be ÷ bp and Let q = ÷ bp
-> e = a – q
-> a – q will be -aq and Let r = -aq
-> e = r
-> e = r will be =er and let s = =er
-> s 

-> Lets put the values back
-> s will be =er
-> =er will be =e-aq
-> =e-aq will be =e-a÷bp
-> =e-a÷bp will be =e-a÷b+cd
-> =e-a÷b+cd



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LINEAR ALGEBRA (Part-2) - Multiplying Matrices

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ছবি
LINEAR ALGEBRA (Part-2) Multiplying Matrices Standard Calculation We can add, subtract, divide or multiply a matrix with a scalar value. These operations will be element wise. Let's consider a 3✖2 Matrix A 3,2 . See below. A 3,2 = [                                     1 2                                     2 3                                     3 1                                     ]                                     Let's add a scalar value 5 with it. A 3,2 = [ A 3,2 = [  A 3,2 = [ 1 2 5✚1  5✚2  6 7 5 ✚ 2 3 =  5✚2 5✚3  = 7 8 3 1 5✚3  5✚1  8 6 ] ]  ] Let's subtract a scalar value 5 with it. A 3,2 = [ A 3,2 = [  A 3,2 = [ 1 2 5➖1  5➖2  4 3 5 ➖ 2 3 =  5➖2 5➖3  = 3 2 3 1 5➖3  5➖1  2 4 ] ]  ] Let's multiply a scalar value 5 with it. A 3,2 = [ A 3,2 = [  A 3,2 = [ 1 2 5❌1  5❌2  5 10 5 ❌ 2 3 = 5❌2 5❌3  = 10 15 3 1 5❌3  5❌1  15 5 ] ]  ] Let's divide a scalar value 5 with it. A 3,2 = [ A 3,2
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What Is derivative? (Part - 1)

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ছবি
What Is derivative? (Part - 1) Derivative is a simple thing. It’s just the difference of a variable. But how? Think of time, let a person started a journey towards bus stand at time t1 = 3 and reached at t2 = 7. In this case the derivative dt = t2-t1 = 7-3 = 4. Easy! But in real life things are not that easy. Because we have do derive the difference of a variable with respect to another variable unlike our time example where there was only one variable. For example we can see the equation y = x. Here we have to find the difference in y with respect to the change in variable x. In other word we have to find the derivative of y with respect to x which is dy/dx. Fortunately for us this is very easy. Pretty easy right. But we are going to prove it so that we can use the same theory to prove more complex derivatives. So we are going to plot this function into graph. Let’s find some value of x and values of y for the respective value of x below.
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LINEAR ALGEBRA (Part-1) - Scalars, Vectors, Matrices and Tensors

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ছবি
LINEAR ALGEBRA (Part-1) Scalars, Vectors, Matrices and Tensors Scalars Scalars are a single number. like 5 or 8 or 9 etc. you can say age=23 here 23 is a scalar value. Vectors Vectors are a series/array of elements. They are represented between a square bracket with spaces. Like below. ages = [    23    25    33    54 ] Here, [    23    25    33    54 ] is a Column Vector of ages. The Row Vector of ages will look like ages = [23 25 33 54] each element of a vector can be represented by a subscript number like ages 1 =23 or ages 3 =33 etc. the numbers of a vector do not have to be of same thing like. box = [    2    4    8    "wood" ] here the box vector represents, box 1 = height = 2 inch box 2 = width = 4 inch box 3 = weight = 8 gram box 4 = made of = wood Matrix Matrix is a 2D array of elements. Like below. box = [    2    3    2    4    4    4    5    2    8    12    5
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