Understand
Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column).
- Tensors have a rich history, stretching over almost a century, and touching upon numerous disciplines; but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing, statistics, data mining and machine learning.
- This overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors.
- As such, it focuses on fundamentals and motivation (using various application examples), aiming to strike an appropriate balance of breadth {\em and depth} that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and/or developing tensor algorithms and software.