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.
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