|Elements of a square matrix|
|Calculation accuracy (signs after a comma)|
|You entered the following elements of the massif|
|Inverse square matrix|
In this material online the return matrix calculates from square set. Works with complex numbers.
The matrix is called return for a square matrix of A if
where E - a single matrix (i.e. a matrix on the main diagonal of which there are units, and all other elements are equal to zero)
A square matrix A is called degenerate if its determinant is zero, and non-degenerate otherwise .
If the matrix A has the inverse, then this matrix is non-degenerate.
The converse is also true. Every non-degenerate matrix.
has an inverse matrix
Where A ij is the algebraic complement of the matrix
For example, the original matrix
And this is the opposite, with rounding to 4 decimal places
What is the practical value of the inverse matrix? Where can we use it?
The simplest and most illustrative example.
We have a system of equations
We need to express and through and
if we take from the matrix
the opposite, then we get
And therefore our decision looks like this
Using an inverse matrix, for example, we need to create diophantine equations from a common matrix.
Some more examples
The inverse matrix of the original is
Matrix containing expressions
after automatic conversion we get just such a matrix
And its inverse matrix has the following form
Good calculations !!