Vector Definition

There are various mathematical representations, such as scalars, vectors, matrices, and tensors. A scalar can be considered as a number, a decimal, or even a fraction. A matrix can be considered as a rectangular array of numbers. A vector is a collection of numbers that represent some real objects. You can think of a vector as a row in a matrix. A tensor is a general concept that can be comprised of scalars, vectors, and matrices.

The following diagram shows how scalars, vectors, matrices, and tensors are different from each other:

Figure 7.1: Scalars, vectors, matrices, and tensors

Now, try to think about text as follows::

• A letter that is a single unit of an alphabet
• A word that is a series of letters
• A sentence that is a series or words
• A paragraph that is a sequence of words
• A document that is a collection of words, possibly broken down into paragraphs

Each of the preceding units are in text format...