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About What Are Tensors
Product Description Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive. The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily. This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students. From the Author > Free Chapter 1> (Copy/paste the following URL)worldscientific.com/doi/pdf/10.1142/9789811241024_0001> Excerpt (page 4):What do love and tensor have in common?What is love?"Love is when a girl puts on perfume and a boy puts on shaving cologne and they go out and smell each other." (age 5)"Love is when you tell a guy you like his shirt, then he wears it every day." (age 7)"If you want to learn to love better, you should start with a friend who you hate." (age 6)"Love is when mommy sees daddy smelly and sweaty and still says he is handsomer than Robert Redford." (age 8)"Love is when your puppy licks your face even after you left him alone all day." (age 4)"Love is when you kiss all the time. Then when you get tired of kissing, you still want to be together and you talk more." (age 8)"I know my older sister loves me because she gives me all her old clothes and has to go out and buy new ones." (age 4)"I let my big sister pick on me because my mom says she only picks on me because she loves me. So I pick on my baby sister because I love her." (age 4)Each of these answers certainly tells some aspect of the truth.What do love and tensor have in common? Is the love between sisters the same as that between mom and dad, dating teenagers, and dogs and humans? Compare with the question: is the tensor in machine learning the same as those in mathematics and physics?The concept of love is abstract and complex, and it has never been rigorously defined. The tensor is also abstract and complex. It was poorly defined in the past. There are rigorous modern definitions, but at a cost of being more abstract and less intuitive. So the old-fashioned definition is hard to understand because it is not rigorous; the modern definition is hard to understand because it is rigorous. It is the goal of this book to explain the rigorous definitions of tensor in an intuitive way, so that students no longer have to recite those definitions like a parrot.
