What does det mean in physics and math?

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In summary, the determinant of a matrix is mostly used to solve systems of linear equations and is a crucial step in inverting a square matrix. However, it is not the only method for finding the inverse of a matrix and may not always be necessary.
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Sicktoaster
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I'm new to physics and I see "det" used in math a lot. What does it mean?
 
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It means to take the determinant of a matrix.
 
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Yeah, a matrix is a rectangular arrangement of numbers and the details means taking the determinant. Look up matrices and determinants on the net. Or better yet, there's a good course in linear algebra on iTunes u ( the one with Gilbert Strang) check it out
 
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The "determinant" of a matrix is mostly used to solve systems of linear equations. It has multiple uses, but most notably, finding the determinant is a crucial step in inverting a square (##n \times n##) matrix. If you plan on pursuing high level math, physics, or engineering, you'll need to know what the determinant is and how to interpret it.
 
  • #5
AMenendez said:
finding the determinant is a crucial step in inverting a square (##n \times n##) matrix

Is it?
 
  • #6
AMenendez said:
finding the determinant is a crucial step in inverting a square (##n \times n##) matrix
Borek said:
Is it?
I agree with Borek here (in his questioning of your statement about the determinant being a crucial step in inverting a matrix.

Certainly if det(A) = 0, the inverse of A doesn't exist, but for an invertible matrix A, you can find the inverse using Gauss-Jordan without ever taking the determinant. If it turns out that A isn't invertible, the Gauss-Jordan process will end up with a matrix with one or more rows of zeros (instead of the identity matrix) on the left side of your augmented matrix.
 
  • #7
That makes sense. I'm a first-year undergrad and the highest level of math I've had is linear algebra, so I'm just pulling out of the bag of tricks I have so far. Thanks for pointing that out.
 

1. What is the definition of "det"?

"Det" is a mathematical term that stands for determinant. It is a value that can be calculated from a square matrix and has various uses in linear algebra and other fields of mathematics.

2. How is "det" used in linear algebra?

In linear algebra, "det" is used to determine whether a square matrix is invertible or not. It is also used to find the area or volume of a parallelogram or parallelepiped, respectively, with sides defined by the column vectors of the matrix.

3. Can "det" be negative?

Yes, "det" can be negative in some cases. For example, if the matrix has an odd number of negative entries, the determinant will be negative. However, in other cases, such as a 2x2 matrix, the determinant is always positive.

4. Is "det" the same as the trace of a matrix?

No, "det" and trace are two different mathematical concepts. The trace of a matrix is the sum of its diagonal entries, while the determinant is a value calculated from all the entries of the matrix.

5. What are some real-life applications of "det"?

"Det" has various real-life applications, such as in physics, where it is used to calculate the moment of inertia of a rigid body. It is also used in computer graphics to determine the orientation of an object in 3D space. Additionally, "det" is used in economics to analyze input-output models and in chemistry to calculate molecular orbitals.

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