Self-study roadmap for DL/ML

Preliminary

Linear Algebra

How does matrix multiplication work and what is the meaning of those transformations？

1. A matrix can be viewed as a function that transforms vectors. If A represents a linear transformation, and x is a vector, then Ax gives the transformed vector in a space span by column vectors of A.
2. If A represents a linear transformation, and B is a matrix, then AB gives the transformed column vectors of B in a space span by column vectors of A.
3. If A\B both represents linear transformations, the product AB can be interpreted as applying the transformation represented by B first, followed by the transformation represented by A.
4. Consider a matrix A that represents a rotation and a matrix B that represents a scaling. The product AB will first scale a vector and then rotate it.
5. To any full-ranked linear independent matrix, they can be written into . If a matrix left multiply A, It can be seen as first transformed to another vector space, which is much more simple for calculation, and finally transformed back to the original vector space.
6. In neural networks, layers can be represented by matrices, and the multiplication of weight matrices and input vectors represents the transformation of data as it flows through the Linear Algebranetwork.

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