Vandermonde Determinant, what am i doing wrong?

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In summary, the conversation is about a person who made a trivial mistake while using the formula for calculating the determinant of a Vandermonde matrix. They were puzzled by the different polynomial they got compared to the one on the Wikipedia page, which has a term of degree 3. They were also unsure how the determinant of a 3x3 Vandermonde matrix could result in a polynomial with a maximum degree of three. However, since there is no one named Vandermonde Determinant on the platform, they were unlikely to get a reply.
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PsychonautQQ
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EDIT: I figured out what I was doing wrong, trivial mistake. If this could get deleted that would be good.

so using {x,y,z} I'm making a vandermonde matrix; https://en.wikipedia.org/wiki/Vandermonde_matrix. When calculating the determinant by cofactor expansion I calculate the determinant to be the polynomial yz^2 - zy^2 - xz^2 + zx^2 + xy^2 - yx^2.

However, when I use the formula for calculating the determinant on the wikipedia page i get a different polynomial, one that includes a term of degree 3.

How is this possible? What am I doing wrong? How could the determinant of a 3x3 vandermonde matrix possibly be a polynomial with maximum degree three? Help :-(.
 
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I don't think there is anyone here called Vandermond Determinant (Dutch?), sorry, so I don't think you will get a reply.
 
  • #3
WWGD said:
I don't think there is anyone here called Vandermond Determinant (Dutch?), sorry, so I don't think you will get a reply.

Yes, Vandermonde is dutch:
Van = From
Der = The
Mond = Mouth (usually mouth of the human body, but it is likely to mean a place near the end of a river here).
 

FAQ: Vandermonde Determinant, what am i doing wrong?

1. What is a Vandermonde Determinant?

A Vandermonde Determinant is a mathematical expression that represents the determinant of a certain type of square matrix. It is commonly used in algebra and number theory.

2. How is a Vandermonde Determinant calculated?

A Vandermonde Determinant is calculated by taking the product of the diagonal elements of a square matrix, where the elements are the powers of a given set of numbers. For example, if the set of numbers is {a, b, c}, the Vandermonde Determinant would be calculated as (a-b)(a-c)(b-c).

3. What is the significance of the Vandermonde Determinant?

The Vandermonde Determinant has many applications in mathematics and science. It is often used to solve systems of linear equations, interpolate data, and in the study of polynomials and their roots.

4. Can I use a Vandermonde Determinant to solve any type of equation?

No, a Vandermonde Determinant is only useful for certain types of equations, specifically those involving powers of a given set of numbers. It is not a universal solution for all types of equations.

5. What are some common mistakes when calculating a Vandermonde Determinant?

Some common mistakes when calculating a Vandermonde Determinant include forgetting to take the product of the diagonal elements, using incorrect powers of the given numbers, and not considering the correct order of the elements in the determinant.

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