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Matrix Subtraction


To understand the notion of matrix subtraction , first we must know what are the matrices in the field of math . A matrix is ​​a series of symbols and / or numbers that are located in vertical and horizontal lines and that are arranged as a rectangle.

Each of the numbers that make up this arrangement in two dimensions that we call matrix it's called entry , and must be ordered in rows (which are also known by the name of lines) and columns, as mentioned in the previous paragraph. The way to refer to a matrix with a number n of rows and one m of columns is matrix n x m (note that the x is the sign of multiplication, so it reads "by").

It is important to note that the matrices have various applications, some of which are summarized below:

* in computing : since they are characterized by allowing the manipulation of information easily and lightly (without requiring much processing), the matrices are often used for numerical calculations and for the representation of graphs (a set of vertices that are linked through edges and that serve to represent binary type relationships between several elements);

* matrix theory : a branch of mathematics that relates to algebra, statistics, combinatorics and theory of graphs;

* Vector spaces : are structures that are made up of vectors. In this context, if two whose dimensions are finite are taken, an array can be used to make a linear application between them.

With these matrices, different ones can be developed operations : However, certain conditions must be met for operations to be completed. In the case of matrix subtraction , it is essential that the matrices in question have identical dimensions (They must have the same number of columns and rows).

To subtract two matrices, therefore, those components that are placed in it must be subtracted from each other position . Take the example of this first image, with its two matrices.

In this case, following the definition given above, we should complete the following steps to solve the operation. We start with the first column (that is, with the numbers vertically):

2 - 6 = - 4
3 - 2 = 1
5 - (-1) = 6

Then we continue with the second column :

5 - (-2) = 7
2 - 4 = - 2
- 6 - 8 = - 14

Finally, we subtract the elements of the third column :

- 4 - 3 = - 7
1 - 5 = - 4
3 - 5 = - 2

In this way, we only have sort the numbers to get the result this matrix subtraction , as can be seen in this second image.

The subtraction of matrices, in short, consists in subtracting the different components of each matrix, always respecting the place they occupy in the structure. If the matrices had different number of components, the operation cannot be completed. It should be mentioned that the same occurs with the addition (or addition) of matrices. However, there is no restriction with respect to the proportion that must be between the number of rows and columns.

It is known by the name of square matrix to the one that has the same number of columns as of rows, since the appearance they have when graphing them is that of a square. As mentioned in the previous paragraph, it is perfectly possible to subtract (and add) two matrices whose shapes are not square: the important thing is that for each pair there is a corresponding one.

It is essential to understand that both this concept and many others of mathematics can serve us in everyday life, and that it is not a matter of topics for a few with special abilities. It is very likely that most people make matrices more often than they think, even if they do not recognize them as such; after all, it's about a technique to relate and organize data . The subtraction of matrices, as well as other operations, we also usually apply if in two lists of elements corresponding to each other we need to know how much is left of the former once they are affected by the latter.