In this lab, you'll be practicing some interesting properties of a dot product-type matrix multiplication. Understanding these properties will become useful as you study machine learning. The lab will require you to calculate results to provide a proof for these properties.
In this lab you will:
- Demonstrate the distributive, commutative, and associative property of dot products
- Use the transpose method to transpose Numpy matrices
- Compute the dot product for matrices and vectors
- For each property, create suitably sized matrices with random data to prove the equations
- Ensure that size/dimension assumptions are met while performing calculations (you'll see errors otherwise)
- Calculate the LHS and RHS for all equations and show if they are equal or not
# Your code here
# Your code here
# Your code here
Note: supersciptT denotes the transpose we saw earlier
# Your code here
# Your code here
You've seen enough matrix algebra by now to solve a problem of linear equations as you saw earlier. You'll now see how to do this next.