All input and targets in the training set for a neural network training must be represented as tensors (or multi-dimensional arrays). Tensors are actually generalizations of two-dimensional matrices to an arbitrary number of dimensions. Typically, these are floating point tensors or integer tensors. Whatever the raw input data type—image, sound, text—it should be first converted to a suitable tensor representation. This step is called data vectorization. The following are tensors of different dimensions that we will be using frequently in this book:

• Zero-D tensor or scalar: A tensor that contains one single number is called a zero-dimensional tensor, zero-dimensional tensor, or scalar. 
• One-dimensional tensor or vector: A tensor that contains an array of numbers is called a vector or one-dimensional tensor. The number of dimensions of the tensor is also called the axes of the tensor. One-dimensional tensor has exactly one axis.
• Matrices (two-dimensional tensors): A tensor that contains an array of vectors is a matrix, or a two-dimensional tensor. A matrix has two axes (denoted by rows and columns).
• Three-dimensional tensors: By stacking a set of matrices (of same dimensions) in an array, we get a three-dimensional tensor.

By putting three-dimensional tensors in an array, four-dimensional tensors can be created. And so on. In deep learning, generally we play with zero-dimensional to four-dimensional tensors. 

Tensors have three key attributes:

• Dimension or number of axes 
• Shape of the tensor, that is, how many elements the tensor has along each axes
• Data type—whether it's an integer tensor or a floating-type tensor