Linear Algebra Scratchpad
Using Tensorflow.js to help us with the maths
tf = require('@tensorflow/tfjs')
Vectors (please bear with me)
Vectors are a new thing, similar to co-ordinates, but with magnitude and direction. They are relative measures.
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Define example vectors to work with
vector_a = tf.tensor1d([2,2])
vector_b = tf.tensor1d([4,1])
We can do familiar operations, such as addition, subtraction, etc.
These operations happen pairwise
tf.add(vector_a, vector_b).data()
tf.sub(vector_a, vector_b).data()
Our example vectors are setup with 2 dimensions, but there is no limit to the number of dimensions. The operations work on any length / size. The term n-dimensional refers to the fact that the number of dimensions is arbitrary. Try changing the length of our vectors and seeing what happens.
Importantly, geometry also works
Most linear algebra libraries also have helper functions to do this stuff. We can use the Pythagorean theorem to get distances between vectors.
tex`a^2 + b^2 = c^2`
vector_a.norm().data()
Let's verify that number
// 2^2 + 2^2 = c^2 // c^2 = 4 + 4 // c = 8^.5 8**.5
We can use the same process to get a distance between vectors.
tf.sub(vector_a, vector_b).norm().data()
Shapes
You'll often hear people describing shapes in n-dimensional space (also sometimes called hyperspace (pew! pew!).
html`<a href="https://imgflip.com/i/288oe8"><img src="https://i.imgflip.com/288oe8.jpg" title="made at imgflip.com"/></a>`
But seriously, what does that mean?
Math part done!