Types of matrices (Gemini)
Row Matrix:
A matrix with only one row.
Column Matrix:
A matrix with only one column.
Rectangular Matrix:
A matrix where the number of rows and columns are not equal.
Square Matrix:
A matrix where the number of rows equals the number of columns.
Based on Elements
Null Matrix (Zero Matrix):
A matrix where all elements are zero.
Diagonal Matrix:
A square matrix where all elements outside the main diagonal are zero.
Scalar Matrix:
A diagonal matrix where all the diagonal elements are equal.
Identity Matrix (Unit Matrix):
A diagonal matrix with 1s on the main diagonal and 0s elsewhere.
Singleton Matrix:
A matrix with only one element.
Based on Position of Elements
Upper Triangular Matrix:
A square matrix where all elements below the main diagonal are zero.
Lower Triangular Matrix:
A square matrix where all elements above the main diagonal are zero.
Based on Properties
Symmetric Matrix:
A square matrix where the element at position (i, j) is equal to the element at position (j, i).
Skew-Symmetric Matrix:
A square matrix where the element at position (i, j) is the negative of the element at position (j, i).
Orthogonal Matrix:
A square matrix whose transpose is equal to its inverse.
Singular Matrix:
A square matrix whose determinant is zero.
Non-Singular Matrix:
A square matrix whose determinant is not zero.