Lesson 3 of 13 · 7 min
Types of matrices
NCERT §3.3
The counter keeps smaller tables too: one row of prices, one column of today's pen sales, and square tables that compare the classes with each other.
The lesson in notes
In short
Column matrix: exactly one column, order m × 1. Row matrix: exactly one row, order 1 × n.
Square matrix: as many rows as columns, order n × n, called a square matrix of order n.
In a square matrix the entries a₁₁, a₂₂, …, aₙₙ form the (leading) diagonal.
Diagonal matrix: a square matrix whose off-diagonal entries are all zero, that is aᵢⱼ = 0 whenever i ≠ j. The diagonal entries may be anything, including zero.
Scalar matrix: a diagonal matrix whose diagonal entries are all equal to one constant k.
Identity matrix Iₙ: the scalar matrix with k = 1, so aᵢⱼ = 1 when i = j and 0 when i ≠ j. Every identity matrix is scalar, and every scalar matrix is diagonal, but not the other way round.
Zero (null) matrix O: every entry is 0. It can have any order, which is read from the context.