Scalar
A scalar is a number. Eg: 1, 2, 3, etc.
Vector
Vectors can be thought of as an array of numbers where the order of the numbers also matters. They are typically represented by a lowercase bold letter such as x. The individual numbers are denoted by writing the vector name with a subscript indicating the position of the individual member. For example, x1 is the first number, x2 is the second number, and so on. If we want to write the vector with the members explicitly then we enclose the individual elements in square brackets as,
Matrix
A Matrix is an ordered 2D array of numbers and it has two indices. The first one points to the row and the second one to the column. A Matrix can have multiple numbers of rows and columns. Note that a Vector is also a Matrix, but with only one row or one column.
Many calculations such as addition, multiplication, dot product, etc can be performed on a matrix.
Inverse and Transpose
The Matrix inverse and the Matrix transpose are two special kinds of Matrix properties. Again, we will start by discussing how these properties relate to real numbers and then how they relate to Matrices.
Inverse
First of all, to have an inverse the matrix must be “square” (same number of rows and columns). But also the determinant cannot be zero (or we end up dividing by zero)
Transpose
Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.”
