matrices
TRANSCRIPT
- 1. MATRICES AND DETERMINATS
DANIEL FERNANDO RODRIGUEZ
COD: 2073410
PETROLEUM ENGINEERING
2. Definition
A matrixis a rectangular arrangement of numbers.Forexample,
Analternativenotation uses largeparenthesesinstead of box
brackets:
3. The horizontal and vertical lines in a matrix are calledrows and
columns, respectively. Thenumbers in thematrix are
calleditsentriesoritselements. Tospecify a matrix'ssize, a
matrixwithmrows and ncolumnsiscalledanm-by-nmatrixormnmatrix,
whilem and n are calleditsdimensions. Theaboveis a 4-by-3
matrix.
4. TYPES OF MATRICES
Upper triangular matrixIf a square matrix in which all the elements
that are below the main diagonal are zeros. the matrix must be
square.
Lower triangular matrixIf a matrix in which all the elements that
are above the main diagonal are zeros. the matrix must be
square.
5. TYPES OF MATRICES
Determinant of a matrix.The determinant of a matrix A (n, n) is a
scalar or polynomial, which is to obtain all possible products of a
matrix according to a set of constraints, being denoted as [A]. The
numerical value is also known as the matrix module.
EXAMPLE:
6. TYPES OF MATRICES
Band matrix:
In mathematics, particularly in the theory of matrices, a matrix is
banded sparse matrix whose nonzero elements are confined or limited
to a diagonal band: understanding the main diagonal and zero or
more diagonal sides.Formally, an n * n matrix A = a (i, j) is a
banded matrix if all elements of the matrix are zero outside the
diagonal band whose rank is determined by the constants K1 and
K2:Ai, j = 0 if j i + K2, K1, K2 0.
7. TYPES OF MATRICES
Transpose MatrixIf we have a matrix (A) any order mxn, then its
transpose is another array (A) of order nxm where they exchange the
rows and columns of the matrix (A). The transpose of a matrix is
denoted by the symbol "T" and is, therefore, that the transpose of
the matrix A is represented by AT. Clearly, if A is an array of
size mxn, At its transpose will nxm size as the number of columns
becomes row and vice versa.Ifthe matrix A is square, its transpose
is the same size.
EXAMPLE:
8. TYPES OF MATRICES
Two matrices of order n are reversed if your product is the unit
matrix of order n. A matrix has inverse is said to be invertible or
scheduled, otherwise called singular. Properties(A B) -1 = B-1
to-1(A-1) -1 = A(K A) -1 = k-1 to-1(A t) -1 = (A -1) t
Inverse matrix calculation by determining
=Matrix Inverse
= Determinant of the matrix = Matrix attached= Matrix transpose of
the enclosed
9. BASIC OPERATIONS
SUM OR ADITION:
Given the matrices m-by-n, A and B, their sum A + B is the matrix
m-by-n calculated by adding the corresponding elements (ie (A + B)
[i, j] = A [i, j] + B [i, j]). That is, adding each of the
homologous elements of the matrices to add. For example:
10. BASIC OPERATIONS
SCALAR MULTIPLICATIONGiven a matrix A and a scalar c, cA your
product is calculated by multiplying the scalar by each element of
In (ie (cA) [I j] = cA [R, j]).
Example
Properties
Let A and B matrices and c and d scalars.
Closure: If A is matrix and c is scalar, then cA is matrix.
Associativity: (cd) A = c (dA)
Neutral element: 1 A = A
Distributivity:To scale: c (A + B) = cA + cBMatrix: (c + d) A = cA
+ dA
11. BASIC OPERATIONS
The product of two matrices can be defined only if the number of
columns in the left matrix is the same as the number of rows in the
matrix right. If A is an m n matrix B is a matrix n p, then their
matrix product AB is m p matrix (m rows, p columns) given by:
for each pair i and j.
For example:
12. BIBLIOGRAPHY
http://es.wikipedia.org/wiki/Matriz_(matem%C3%A1tica)