Google

A vector can be conceptualized as a fixed-length array of scalars. Mathematically and computationally, vectors are implemented as $$1^{	extrm{st}}$$-order tensors. When vectors represent data from real-world datasets, their scalar values hold real-world significance, such as a vector representing a patient where its components correspond to specific vital signs.

Vector

A data scientist is creating a simple computer model to represent different fruits. The model must represent each fruit using three numerical features, always in this specific order: (1) average weight in grams, (2) sugar content in grams, and (3) water content in grams. How would this model represent an apple that has an average weight of 150g, a sugar content of 19g, and a water content of 129g?

Analyze the two data structures described in the case study below. Which one can be directly represented as a mathematical vector? Justify your answer by explaining the key properties that a data structure must have to be considered a vector.

Identifying Vector Representations in Data

A vector, denoted by a bold lowercase letter such as $$\mathbf{x}$$, can be defined by explicitly listing its elements. This component-wise representation is an ordered sequence of scalars, commonly written as $$\mathbf{x} = (x_1, x_2, \dots, x_n)$$, where $$n$$ represents the vector's dimensionality.

Component-wise Notation for a Vector

A computer program needs to store the coordinates of a point in a 3-dimensional space. The coordinates are an x-value, a y-value, and a z-value, and their order is crucial (x, then y, then z). Which of the following mathematical structures is the most appropriate and direct way to represent these coordinates?

Learn Before

Related