This document defines and provides examples of different types of matrices including row, column, rectangular, transpose, opposite, square, symmetrical, identical, reverse, and triangular matrices. It also covers matrix operations such as addition, multiplication, and inverse matrices. Key points are that a matrix is an arrangement of numbers or other items in rows and columns, and different types of matrices are classified based on their size, elements, and properties such as symmetry.

1. MATRICES
NORAIMA NAYARITH ZARATE GARCIA
COD. 2073173
ING. DE PETROLEOS
UNIVERSIDAD INDUSTRIAL DE SANTANDER

2. MATRICES
 An matrix is a set of items of any nature, but in general,
numbers are usually arranged in rows and columns.
Order matrix is called "m × n" to a set of elements Ɑij
rectangular arranged in m rows and n columns.

3. TYPES OF MATRICES
TYPES OF MATRIX DEFINITION EXAMPLE
ROW That matrix has a single row,
with order 1 × n
COLUMN That matrix has a single column,
and its order m × 1
RECTANGULAR That array that has different
number of rows and columns, and
its order m × n,
TRANSPOSE Given a matrix A, is called the
transpose of the matrix A is
obtained by changing orderly
rows of columns.
Is represented by AT or AT
OPPOSITE The opposite of a given matrix is
the result of replacing each
element by its opposite. The
opposite of A is-A.
SQUARE That parent has an equal number
of rows and columns, m = n,
saying that the matrix is of order
n.
Main diagonal: are the elements
Ɑ11, Ɑ22, ..., Ɑnn
Secondary Diagonal: Ɑij are the
elements to Ɑij , i + j = n +1
Trace of a square matrix is: the
sum of main diagonal elements of
tr A.

4. TYPES OF MATRICES
TYPES OF MATRIX DEFINITION EXAMPLES
SYMMETRICAL It is a square matrix equals its
transpose.
A = At, Ɑij = Ɑji
IDENTICAL Es una matriz cuadrada que tiene
todos sus elementos nulos excepto los
de la diagonal principal que son
iguales a 1. Tambien se denomina
matriz unidad.
REVERSE We say that a square matrix has an
inverse, A-1 if it is verified that:
A · A-1 = A-1 ° A = I
TRIANGULAR It is a square matrix that has all the
elements above (below) the main
diagonal to zero.

5. OPERATIONS WITH MATRICES
 SUM:
The sum of two matrices of the same size (equidimensional)
another mat is another matrix
EXAMPLE:
PROPERTIES:
o Associations: A + (B + C) = (A + B) + C
· Commutative: A + B = B + A
· Elem. Neutral: (0m × n zero matrix), 0 + A = A +0 = A
· Elem. symmetric (opposite-matrix A), A + (-A) = (-A) + A = 0

6. PRODUCT MATRIX
 Given two matrices A = (Ɑij) m × n and B = (bij) p × q = p were n=p , the
number of columns in the first matrix equals the number of rows of the
matrix B, is defined A · B product as follows:
 EXAMPLE:

7. INVERSE MATRIX
 Inverse matrix is called a square matrix An and represent the A-1, a
matrix that verifies the following property: A-1 ° A = A ° .A-1 = I
PROPERTIES :

8. BIBLIOGRAPHY
 CHAPRA , STEVEN C. Y CANALE, RAYMOND
P. Numerics Mathods for Engineers. McGraw
Hill 2002.
 es. Wikipedia. Org/wiki.
 SANTAFE, Elkin R. “Elementos básicos de
modelamiento matemático”.
 Clases -universidad de Santander año-2009.