mathematics

Triangular matrix :  A matrix is said to be a triangular matrix if, either 1.every element above principal diagonal is zero. 2.1.every element below principal diagonal is zero.  upper triangular matrix : A matrix is said to be upper triangular if, every element below principal diagonal is zero.  Lower triangular matrix : matrix is said to be a triangular matrix if,  every element above principal diagonal is zero. Note ( both of eg. listed above) transpose of matrix : if A is a matrix of type m×n obtained by interchanging it's rows and column is called tranpose of A and is denoted by A' or A^T.

Matrices chapter 1   Matrix :A set of m×n number arranged in the form of ordered set of m rows,  each row consisting of n numbers and enclosed in the bracket [] is called m×n type of matrix.  for eg.  a11   a12.. .. . .. .. .a1n                      a21   a22.  ... .. .. ..a2n                               ..... .. ... ..  .. .. . .. ... ...                              am1   am2 .. .  .. amn          m×n Rectangular Matrix :  m×n matrix is said to be rectangular matrix if m not equal to n.  for eg.  1   2                             ...