From the course: Machine Learning Foundations: Linear Algebra
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Composition or combination of matrix transformations
From the course: Machine Learning Foundations: Linear Algebra
Composition or combination of matrix transformations
- We have experienced basic linear transformations like rescaling, rotation, and inversion. The great thing in linear algebra is that we can combine together any number of different linear transformations to get a new linear transformation. We call it Composition of Linear Transformation. Since any linear transformation can be represented with a matrix, any two or more composed linear transformations can also be represented as matrices. This process is extremely useful in machine learning. Imagine we have to compute the result of ten thousand linear transformations operating on a vector. It becomes computationally expensive, as you have to apply ten thousand sequential functions. On the other hand, if we find the matrix that represents the composition of ten thousand linear transformations, it comes down to a couple of numbers and computations. Lets take a look at the composition of two linear transformations A B V,…
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