Question

who many types of matrices

Answer 1

different types of matrices: row matrix, column matrix, zero matrix, square matrix, diagonalmatrix, unit matrix and equal matrices. A matrix is a rectangular array of numbers. The size or dimension of amatrix is defined by the number of rows and columns
In mathematics, a square matrix is a matrixwith the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation.
Diagonal matrix is a matrix in which non principle diagonal elements are zero. It is not necessary that in diagonal matrix principle diagonal elements must be non zero. Hence square null matrix is also considered as a diagonal matrix. Scalar and unit matrix are special types of diagonal matrices.

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be triviallydetermined by the context.
Definition. If a is an element of matrix A and b is element of matrix B, then the matrix A and B are equal only if a = b for all i and j values. Two matrices to be equal, their order must be the same. If two matriceshave their corresponding elements equal, then they are called equal matrices.

Answer 2

Answer:

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

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