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Introduction to Matrices: Basics and Types

• Matrices are important in GATE exams, with at least one fashion and sometimes two questions on the topic.
• A matrix is a two-dimensional array that is represented as "M x N," where M is the number of rows and N is the number of columns.
• Rectangular matrices have M ≠ N, while square matrices have M = N.
• The unit matrix is a square matrix with all principal diagonal elements equal to one and all other elements equal to zero.
• The null matrix is a matrix in which all elements are zero.
• Row matrices have only one row, while column matrices have only one column.
• A submatrix is obtained by eliminating some rows and/or columns from a given matrix.
• The principal submatrix is a square submatrix in which the principal diagonal elements also occur in the principal diagonal of the original matrix.
• From a square matrix, if exactly one row and one column are eliminated, the resulting matrix is also a square matrix.
• The resulting submatrix is a principal submatrix if its principal diagonal elements also occur in the principal diagonal of the original matrix.
• Not all combinations of eliminated rows and columns will result in a principal submatrix.
• The properties of matrices are important for matrix operations such as finding the matrix inverse and matrix multiplication.