A determinant is a real number associated with every
square matrix. I have yet to find a good English definition for what
a determinant is. Everything I can find either defines it in terms of
a mathematical formula or suggests some of the uses of it. There's
even a definition of determinant that defines it in terms of itself.
The determinant of a square matrix A is denoted by "set A" or | A |. Now, that last one looks like the absolute value of A, but you will have to apply context. If the vertical lines are around a matrix, it means determinant.
The line below shows the two ways to write a determinant.
The determinant of a square matrix A is denoted by "set A" or | A |. Now, that last one looks like the absolute value of A, but you will have to apply context. If the vertical lines are around a matrix, it means determinant.
The line below shows the two ways to write a determinant.
|
3 |
1 |
= |
set |
|
3 |
1 |
|
|
5 |
2 |
|
5 |
2 |
|
Determinant of a 2×2 Matrix
The determinant of a 2×2 matrix is found much like a pivot operation. It is the product of the elements on the main diagonal minus the product of the elements off the main diagonal.|
a |
b |
= ad - bc |
|
c |
d |
Properties of Determinants
- The determinant is a real number, it is not a
matrix.
- The determinant can be a negative number.
- It is not associated with absolute value at all
except that they both use vertical lines.
- The determinant only exists for square matrices
(2×2, 3×3, ... n×n). The determinant of a 1×1 matrix is that
single value in the determinant.
- The inverse of a matrix will exist only if the
determinant is not zero.
