Matrices and Vectors
Matrices are 2-dimensional arrays:
The above matrix has four rows and three columns, so it is a 4 x 3 matrix.
A vector is a matrix with one column and many rows:
So vectors are a subset of matrices. The above vector is a 4 x 1 matrix.
Notation and terms:
- refers to the element in the th row and th column of matrix .
- vector with 'n' rows is referred to as an 'n'-dimensional vector.
- refers to the element in the th row of the vector.
- In general, all our vectors and matrices will be 1-indexed. Note that for some programming languages, the arrays are 0-indexed.
- Matrices are usually denoted by uppercase names while vectors are lowercase.
- "Scalar" means that an object is a single value, not a vector or matrix.
- refers to the set of scalar real numbers.
- refers to the set of n-dimensional vectors of real numbers.
- refers to the set of matrices of real numbers.