# Calculate item from n-size cross product without creating product?

• SophieP
In summary, the conversation is about finding a specific set in a cross product without creating the entire product. The example given is using an array of length 512 and a specified number of times to cross-product against itself. The term "cross product" is later corrected to "Cartesian product."
SophieP
Hi all,

I'm trying to work out how I can get the set at specific index in a cross product without creating the whole product.

For instance:

I have array A of length 512

I also have a number that specifies how many times that array needs to be 'cross-producted' against itself.

This gives me a potentially huge set of sets. I need to be able to work out what the set is at a particular point, without iterating through the entire cross product creation procedure.

What doew "cross product" mean in this context?

Hi Mathman,

As an example:

A = [1, 2, 3, 4]

gives:
1,1
1,2
1,3
1,4
2,1
2,2
2,3
2,4
3,1
3,2
3,3
3,4
4,1
4,2
4,3
4,4

I've just noticed that I meant to say Cartesian product, sorry!

Last edited:

## 1. How do I calculate an item from a n-size cross product without creating the product?

To calculate an item from a n-size cross product without creating the product, you will need to use the cross product formula. This formula involves taking the determinant of a matrix composed of the vectors in the cross product. This can be done by hand or using a calculator.

## 2. What is a cross product?

A cross product is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both of the original vectors. It is commonly used in physics and engineering to calculate the direction and magnitude of a force or torque.

## 3. Why is it important to calculate an item from a n-size cross product without creating the product?

Calculating an item from a n-size cross product without creating the product can save time and computational resources. In some cases, creating the full product may be unnecessary and only the specific item is needed for a particular calculation or analysis. Additionally, calculating without creating the product may provide more accurate results as it avoids rounding errors that can occur when working with large numbers.

## 4. Can I use software or tools to calculate an item from a n-size cross product without creating the product?

Yes, there are many software programs and online tools available that can perform cross product calculations. These tools use the cross product formula and can quickly and accurately calculate an item from a n-size cross product without creating the full product. However, it is important to understand the underlying math and principles behind the calculation to ensure accurate results.

## 5. What are some practical applications of calculating an item from a n-size cross product without creating the product?

Calculating an item from a n-size cross product can have many practical applications in fields such as physics, engineering, and computer graphics. It can be used to determine the direction and magnitude of forces, to calculate the torque on an object, or to determine the orientation of an object in 3D space. It can also be used in computer graphics to create 3D models and animations.

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