Understanding Determinants: Calculation and Function

  • Thread starter Gear300
  • Start date
  • Tags
    Determinant
In summary, the determinant is a mathematical tool used to determine the invertibility of a square matrix and has various other applications such as Cramer's rule. The general method for calculating the determinant is through the method of cofactors. As for learning the fundamentals of matrices, Paul's online linear algebra notes are recommended. Additionally, a lattice point is a point with integer coordinates and further information can be found in the Intro to Lattice Points website.
  • #1
Gear300
1,213
9
What does a determinant do exactly (what is it)? And what is the general method of calculating it?
 
Physics news on Phys.org
  • #2
The determinant is mainly used to determine whether or not a square matrix is invertible. There are other applications as well. (ie. Cramer's rule for determining solutions to a system of linear equations)

The method used is generally the http://tutorial.math.lamar.edu/Classes/LinAlg/MethodOfCofactors.aspx" (note link)
 
Last edited by a moderator:
  • #3
hmm...I see...I've practically forgotten the concept of matrices, but thanks. If possible, do you know of a site that simply goes through the fundamentals of matrices? And (this question is slightly random)...what is a lattice point?
 
  • #5
Thanks for the help.
 

FAQ: Understanding Determinants: Calculation and Function

What is a determinant?

A determinant is a mathematical value that can be calculated from the elements of a matrix. It is used to determine various important properties of a matrix, such as its invertibility and the number of solutions to a system of linear equations.

How is a determinant calculated?

The calculation of a determinant involves a specific formula that depends on the size of the matrix. For a 2x2 matrix, the determinant is calculated by multiplying the elements in the main diagonal and then subtracting the product of the elements in the other diagonal. For larger matrices, the calculation involves finding the sum of products of elements in specific patterns. There are various methods and algorithms available for calculating determinants.

What is the significance of a determinant?

Determinants have various important applications in mathematics and science. They are used to determine whether a matrix is invertible, which is necessary for solving systems of linear equations. They also play a crucial role in calculating eigenvalues and eigenvectors, which are important in areas such as physics and engineering.

Can a determinant be negative or zero?

Yes, a determinant can be negative or zero. The sign of a determinant depends on the arrangement of the elements in the matrix. If the elements are arranged in a way that the determinant is negative, it indicates that the matrix is not invertible. If the determinant is zero, it means that the matrix is singular, which also means it is not invertible.

How is a determinant used in solving systems of equations?

Determinants are used to determine whether a system of linear equations has a unique solution, no solution, or infinitely many solutions. If the determinant of the coefficient matrix is non-zero, it means the system has a unique solution. If the determinant is zero, the system either has no solution or infinitely many solutions, which can be further determined by solving the system using other methods.

Similar threads

Replies
2
Views
598
Replies
4
Views
656
Replies
1
Views
1K
Replies
5
Views
942
Replies
2
Views
167
Replies
3
Views
1K
Back
Top