Matrix Multiplication is a different world.

Ever wondered what happens when you multiply a vector to a matrix? What does a matrix represent? What do we get after the multiplication? Let’s view these questions from a Data Science perspective.

In data science, we come across a lot of matrix multiplication, do you know that a matrix is just another world where things may work differently?
I mean, in our natural world the coordinates are so simple, any object can be located using the X, Y, and Z-axis, yeah?

Have a look at this picture in our natural world:

That’s a beautiful and healthy avocado right there.
But avocados don’t look the same in all the worlds that do not share the same coordinate logic as ours.

The same Avocado in a world using different shapes and sizes:

It’s the same avocado with a transformed structure and the guy who transformed this avocado is called Mr. Matrix.

Well, Mr. Matrix is the guy who takes in avocado and produces a new version of the avocado and the version depends upon the world in which Mr. Matrix lives.

Here is another world of Mr. Matrix producing a new version of avocado.

Wow, you see what Mr. Matrix has done to our avocado this time? Clearly, we should choose the values of Mr. Matrix carefully.

The avocado is the vector that Mr. Matrix takes in for multiplication and returns a new vector that may be quite different than the original.

The vector [1, 2] is our original vector which gets into the world of Mr. Matrix, the multiplication happens, and then Mr. Matrix spits out a new transformed vector [0, 3]. Think of this event as the movement of the original vector from [1, 2] to a new position [0, 3] caused by the Matrix.

So now that you understand the job of Mr. Matrix, here is a couple of things to note:

Just make sure that the dimensions of the input vector (avocado) and Mr. Matrix are the same so that the vector gets accepted in the world of Mr. Matrix.

Honestly, the visuals around these concepts can greatly help us understand the power of Matrices and other topics in Machine learning and Mathematics.
And the aim of this article is to push you a little further in your data science journey. And please don’t get intimidated by Linear Algebra, we’re all in this together. 🙋

Related posts:

Kristin Knight Pace — Finishing the 2015 Yukon Quest a 1,000 Mile Sled Dog Race and the 2016 Iditarod. In 2009, after a crippling divorce that left her heartbroken and directionless, Kristin decided…

The largest technology fund in the world just took a significant stake in the most important chip company in the world. Interestingly enough, neither company is from Silicon Valley. In this global…