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Study Notes

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.

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