what are the row matrices and column matrices.can they ever be equal?what are the general forms for their orders?
Answers
Linear Algebra
Seifedine Kadry, in Mathematical Formulas for Industrial and Mechanical Engineering, 2014
3.2 Basic Types of Matrices
1.
Row matrix: A matrix having a single row. Example: [ 1 −2 4 ].
2.
Column matrix: A matrix having a single column. Example: [ −1 2 5 ].
3.
Null matrix: A matrix having all elements zero. Example: ( 0 0 0 0 ). A null matrix is also known as a zero matrix, and it is usually denoted by 0.
4.
Square matrix: A matrix having equal number of rows and columns. Example: The matrix ( 3 −2 −3 1 ) is a square matrix of size 2×2.
5.
Diagonal matrix: A square matrix, all of whose elements except those in the leading diagonal are zero. Example: ( 2 0 0 0 −3 0 0 0 5 ).
6.
Scalar matrix: A diagonal matrix having all the diagonal elements equal to each other. Example: [ 3 0 0 0 3 0 0 0 3 ].
7.
Unit matrix: A diagonal matrix having all the diagonal elements equal to 1.
Example: [ 1 0 0 1 ], [ 1 0 0 0 1 0 0 0 1 ], … A unit matrix is also known as an identity matrix and is denoted by the capital letter I.
8.
Triangular matrix: A square matrix, in which all the elements below (or above) the leading diagonal are zero.
Example: ( 3 1 4 0 2 −1 0 0 4 )and( 1 0 0 2 3 0 4 −1 5 ) are upper triangular and lower triangular matrices, respectively.
9.
Symmetric matrix: A square matrix [aij] such that aij=aji∀i&j. Example: [ 2 1 −3 1 4 5 −3 5 0 ].
10.
Skew-symmetric matrix: A square matrix [aij] such that aij=−aji∀i&j.
Example: [ 0 2 3 −2 0 1 −3 −1 0 ]. Note that the elements in the leading diagonal of a skew-symmetric matrix are always zero.