Scalar

In physics, a scalar is a mathematical entity that is fully described by a magnitude (or numerical value) alone.
For example, `a = 10.5` is a scalar. There is no other value associated with a scalar, just one single numerical value.

Vector

In physics, the official definition of a vector is a mathematical entity that is fully described by both a magnitude and a direction.
For example, wind speed = 100 miles/hour, Northeast direction. In simple mathematical terms, vectors have multiple values. For example, `b = [10, 20]` is a vector. By this definition, any array of size greater than 1 is a vector.

One-dimensional Array

A one-dimensional array is a type of linear array that has all elements in either one row or one column. Accessing its elements involves a single index position, which can represent either a row or a column index.
For example, a = [1, 2] is a one-dimensional array. Note that this array can have elements in either one row or one column. Using a[0] provides the value of the first element.

Multidimensional Array

A multidimensional array is a type of array structure that has elements represented in both rows and columns. Accessing its elements involves 'n' number of indices, where 'n' denotes the dimension of the array.
For example, b = [[1, 2, 4], [4, 4, 6]] is a 2-dimensional array, as it has two rows and three columns. To access the element in the first row, third column, you use the notation b[0][2].

Array Rank

The number of dimensions is the rank of the array.
For example, if `a = [1, 2, 3]`, then 'a' is of rank 1. If `b = [[1, 2, 4], [4, 4, 6]]`, then 'b' is of rank 2, and so on.

Array Shape

The shape of an array is a tuple of integers giving the size of the array along each dimension.
For example, if `a = [1, 2, 3]`, then 'a' has a shape of (3,). If `b = [[1, 2, 4], [4, 4, 6]]`, then it has a shape of (2, 3).

Array Size

The number of elements in an array determines the size of the array.
For example, `a = [1, 2]` has a size of 2. `b = [[2, 3, 4], [5, 6, 7]]` has a size of 6.

KDE - Kernel Density Estimation

Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths. In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable. Kernel density estimation is a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. Reference: https://en.wikipedia.org/wiki/Kernel_density_estimation