In this section, we will introduce linear transformations. Linear transformations are the backbone of modeling with ANNs. In fact, all the processes of ANN modeling can be thought of as a series of linear transformations. The working components of linear transformations are scalars, vectors, matrices, and tensors. Operations such as addition
, transposition
, and multiplication
are performed on these components.
Scalars, Vectors, Matrices, and Tensors
Scalars
, vectors
, matrices
, and tensors
are the actual components of any deep learning model. Having a fundamental understanding of how to utilize these components, as well as the operations that can be performed on them, is key to understanding how ANNs operate. Scalars
, vectors
, and matrices
are examples of the general entity known as a tensor
, so the term tensors
may be used throughout this chapter but may refer to any component. Scalars
, vectors
, and matrices
refer to tensors
with a specific number...