data representations for neural networks in the previous examplewe started from data stored in multidimensional numpy arraysalso called tensors in generalall current machine-learning systems use tensors as their basic data structure tensors are fundamental to the field--so fundamental that google' tensorflow was named after them so what' tensorat its corea tensor is container for data--almost always numerical data soit' container for numbers you may be already familiar with matriceswhich are tensorstensors are generalization of matrices to an arbitrary number of dimensions (note that in the context of tensorsa dimension is often called an axisscalars ( tensorsa tensor that contains only one number is called scalar (or scalar tensoror -dimensional tensoror tensorin numpya float or float number is scalar tensor (or scalar arrayyou can display the number of axes of numpy tensor via the ndim attributea scalar tensor has axes (ndim = the number of axes of tensor is also called its rank here' numpy scalarimport numpy as np np array( array( ndim vectors ( tensorsan array of numbers is called vectoror tensor tensor is said to have exactly one axis following is numpy vectorx np array([ ] array([ ] ndim this vector has five entries and so is called -dimensional vector don' confuse vector with tensora vector has only one axis and has five dimensions along its axiswhereas tensor has five axes (and may have any number of dimensions along each axisdimensionality can denote either the number of entries along specific axis (as in the case of our vectoror the number of axes in tensor (such as tensor)which can be confusing at times in the latter caseit' technically more correct to talk about tensor of rank (the rank of tensor being the number of axes)but the ambiguous notation tensor is common regardless matrices ( tensorsan array of vectors is matrixor tensor matrix has two axes (often referred to rows and columnsyou can visually interpret matrix as rectangular grid of numbers this is numpy matrixlicensed to