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# Matrices

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### Matrices

1. 1. MATRICES NORAIMA NAYARITH ZARATE GARCIA COD. 2073173 ING. DE PETROLEOS UNIVERSIDAD INDUSTRIAL DE SANTANDER
2. 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. 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. 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. 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. 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. 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. 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.