matrix - a table, which is filled with a certain set of numbers in a certain order.This term was coined by eminent British scientist theorist James Sylvester.He is one of the founders of the theory of the application of these mathematical elements.
To date, they have found widespread use during various calculations, which are based on a method such as, for example, by finding the inverse matrix in the various fields of human activities.This method is based on determining the unknown parameters of the various equations and is often used during the economic calculations.
There are special cases of these data mathematical components: lower case, a column, zero, square, diagonal, single.Lowercase consists of only one row of elements, and a column - of a single column of numbers.Zero - all the elements are equal to 0. The square of the mathematical element number of columns equal to the number of lines.In turn, in the diagonal, located on the main diagonal elements other than "0", and the others it must be equal to "0".Unit - is a subspecies of the diagonal matrix.It is located on the main diagonal only '1'.
matrices Examples:
where: Ak - a generic term, aij - elements,
(a) -2-order;
(b) - lower case;
(c) -3-order;
(d) - an example of a single table of order 2;
Also, there is an inverse matrix, the definition of which is as follows.When multiplied by the feedback obtained the original table unit.A variety of techniques that ensures that the inverse matrix.The simplest of them is based on the definition of the determinant and cofactors (also sometimes referred to as determinant).
determinant of the matrix is an expression a11a22-a12a21, he is designated as follows: |A|.This formula is valid for a table corresponding to the second order.There are formulas for determinants of matrices of higher order.Mandatory condition for the existence of the determinant - the table should be square.In practice, this element of this theory is most often used in such a procedure as finding the inverse matrix.
second important component that can be used to find the values of its elements is the cofactor.It is calculated by the formula: Aij = (- 1) i + j * Mij, wherein M - is minor.In fact - this is an additional determinant of which may be obtained by mental remove the row and column in which the element is located.For example, for a table, according to the second order, which is shown above in the text, the element a11 is the algebraic complement element a22.
Finding the inverse matrix is carried out in 3 stages.At the first stage the determinants.The next step - all the cofactors, which are then recorded in accordance with its indexes, and it turns the table cofactors.At the final stage of an inverse matrix, finding that ends by multiplying each algebraic complement the determinants.
most commonly used matrix during the economic calculations.With their help, you can easily and quickly process large amounts of information.Thus the end result will be presented in readable form.
Another area of human activity, in which the matrix also found wide application - a simulation of 3D-images.These tools are integrated into modern packages for the implementation of 3D-models and allow designers to quickly and accurately perform the necessary calculations.The most prominent representative of such systems is the Compass-3D.
Another program, which integrates tools for such calculations, is Microsoft Office, and more specifically - spreadsheet Excel.
