- matrix dimension = no of rows * columns
- matrix is numbers written in rows and columns
- Vector is a n*1 matrix
Matrix addition and subtraction
- We can only add or subtract matrices of same dimension and result is matrix of same dimension
Multiplication
(3*2 ) * (2*1) = 3*1 matrix First row -> 1*1+ 3*5
We can now pose h(x) as a matrix
represent h(x) into matrix
now we can do
- for (i=1 to 1000)
- prediction(i) = .... and train our set
Matrix matrix multiplication
Competing hypothesis
- Apply all 3 hypothesis simultaneously
- You can get prediction of each hypothesis in resulting matrix
Matrix mult is not commutative
But matrix mult is associative
- a*b*c = (a*b)*c = a*(b*c)
Identity matrix (1's along diagonals)
identity property:
A.I = I.A = A
Inverse and Transpose
- in maths we have 3*3(Inverse) = 1(Identity) ...-> 3*1/3 = 1
- number 0 does not have inverse in real numbers
- AA(inverse) = A(inverse)A = I
Note: only square matrices have inverses
If A is matrix with all 0 it does not have an inverse
intuition matrix does not have inverse (singular matrix, degenerate matrix) if its too close to 0
Transpose
