Scalars : A scalar is just a single num ber, in con trast to most of the other ob jects studied in linear algebra, whic h are usually arrays of m ultiple num bers. W e write scalars in italics. W e usually give scalars low er-case v ariable names. When we in tro duce them, w e sp ecify what kind of num b er they are. F or 31 CHAPTER 2. LINEAR ALGEBRA example, w e migh t sa y “Let s ∈ R b e the slop e of the line,” while deﬁning a real-v alued scalar, or “Let n ∈ N b e the num b er of units,” while deﬁning a natural n um b er scalar
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chapter will completely omit many important linear algebra topics that are not essential for understanding deep learning. 2.1 Scalars, Vectors, Matrices and Tensors The study of linear algebra involves several types of mathematical objects: • <span>Scalars : A scalar is just a single number, in contrast to most of the other objects studied in linear algebra, which are usually arrays of multiple numbers. We write scalars in italics. We usually give scalars lower-case variable names. When we introduce them, we specify what kind of number they are. For 31 CHAPTER 2. LINEAR ALGEBRA example, we might say “Let s ∈ R be the slope of the line,” while deﬁning a real-valued scalar, or “Let n ∈ N be the number of units,” while deﬁning a natural number scalar. • Vectors : A vector is an array of numbers. The numbers are arranged in order. We can identify each individual number by its index in that ordering. Typically we give vectors lower ca