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Maths Exercices

Definitions

  1. Two matrices A and B of the same order whose corresponding entries are equivalent are considered equal. That is: aij=bij i=1,...,n ; j=1,2,...,m.
  2. A square matrix is a matrix which has the same number of rows and columns.
  3. The main diagonal of a matrix is formed by the elements of a matrix starting in the upper left corner and proceeding down and to the right (aii).
  4. A matrix with all-zero entries below the top-left-to-lower-right diagonal is called upper triangular.
  5. A matrix with all-zero entries over the top-left-to-lower-right diagonal is called lower triangular.
  6. A matrix with non-zero entries only on the diagonal is called diagonal.
  7. A diagonal matrix whose non-zero entries are all 1's is called an identity matrix.
    The 3 × 3 identity is denoted by I3 (pronounced as "eye-three" or "eye-sub-three"); similarly, the 4 × 4 identity is I4 and the 5 × 5 identity matrix is I5.
  8. The transpose of a Matrix A is a matrix which is formed by turning all the rows of the given matrix into columns and vice-versa. The transpose of matrix A is written AT.
Matrix with only one row
Matrix with only one column
Upper triangular
Lower diagonal
Diagonal