MATRICESNORAIMA NAYARITH ZARATE GARCIA

COD. 2073173

ING. DE PETROLEOS

UNIVERSIDAD INDUSTRIAL DE SANTANDER

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.

TYPES OF MATRICESTYPES 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.

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.

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

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:

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 :

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.