LINALG — Matrix multiplication
Matrix multiplication as composition — 3Blue1Brown
The composition, or the mixture of the transformations is matrix multiplication.
Concept outline
When I first encountered this concept, I came up with a sentence: “The end justifies the means”. Let’s look at some matrices.
Here, we are going to rotate and sheer the vector in written order. Note that we should follow where i-hat and j-hat lands, just like the post before.
If we go through this 2 steps of process, the i-hat and j-hat will be rotated and sheared, and land there. However, we can directly move i-hat and j-hat to the landing point, not needing to go through that 2 steps of process.
Because it has the same effect.
The final product(landing point of i-hat & j-hat) is the same, we squished 2 steps into 1.
What should we remember is that order matters here.
Calculating matrix multiplication
