what is matrix? How many type of matrices?
Answers
Answer:A matrix is a rectangular array of numbers. The size or dimension of a matrix is defined by the number of rows and columns it contains. Matrices is plural for matrix.
A matrix may be classified by types. It is possible for a matrix to belong to more than one type.
A row matrix is a matrix with only one row.
Example: E is a row matrix of order 1 × 1
Example: B is a row matrix of order 1 × 3
A column matrix is a matrix with only one column.
Example: C is a column matrix of order 1 × 1
A column matrix of order 2 ×1 is also called a vector matrix.
Example: D is a column matrix of order 2 × 1
Step-by-step explanation:
Answer:
Step-by-step explanation:Type of Matrix Details
Row Matrix A = [aij]1×n
Column Matrix A = [aij]m×1
Zero or Null Matrix A = [aij]mxn where, aij = 0
Singleton Matrix A = [aij]mxn where, m = n =1
Horizontal Matrix [aij]mxn where, n > m
Vertical Matrix [aij]mxn where, m > n
Square Matrix [aij]mxn where, m = n
Diagonal Matrix A = [aij] when i ≠ j
Equal Matrix A = [aij]mxn and B = [bij]rxs where, aij = bij, m = r, and n = s
Triangular Matrices Can be either upper triangular (aij = 0, when i > j) or lower triangular (aij = 0 when i < j)
Singular Matrix |A| = 0
Non-Singular Matrix |A| ≠ 0
Symmetric Matrices A = [aij] where, aij = aji
Skew-Symmetric Matrices A = [aij] where, aij = aji
Hermitian Matrix A = Aθ
Skew – Hermitian Matrix Aθ = -A
Orthogonal Matrix A AT = In = AT A
Idempotent Matrix A2 = A
Involuntary Matrix A2 = I, A-1 = A
Nilpotent Matrix ∃ p ∈ N such that AP = 0