Is there a connection between cross product and determinant?

Click For Summary
SUMMARY

The discussion confirms that the cross product can be derived from the determinant of a 3x3 matrix, emphasizing that this relationship is not coincidental but rather a fundamental aspect of vector mathematics. Additionally, it clarifies the distinction between the wedge product and the cross product, stating that the wedge product generalizes the cross product to any vector space and is defined on forms, while the cross product is specifically defined for vectors.

PREREQUISITES
  • Understanding of 3x3 matrices and determinants
  • Familiarity with vector operations
  • Knowledge of differential forms
  • Concept of vector spaces
NEXT STEPS
  • Study the properties of determinants in linear algebra
  • Learn about the mathematical definition and applications of the wedge product
  • Explore the geometric interpretations of the cross product
  • Investigate the relationship between vector spaces and forms in advanced mathematics
USEFUL FOR

Mathematicians, physics students, and anyone interested in advanced vector calculus and linear algebra concepts.

kidsasd987
Messages
142
Reaction score
4
Is this just a coincidence that cross product can be found from determinant of 3*3 matrix? what is the differences between wedge product and cross product?Thanks.
 
Physics news on Phys.org
Is this just a coincidence that cross product can be found from determinant of 3*3 matrix?
No.
It is another way of writing the definition.

what is the differences between wedge product and cross product?
https://www.physicsforums.com/threads/wedge-product-cross-product.117231/
Basically the wedge product is a generalization of the cross-product to any vector space.
 
For one, the wedge product is defined on forms, and the cross-product is defined on vectors.
 

Similar threads

Difference between scalar and cross product
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why is the Cross Product Used in Mathematics? Understanding its Role and History
  • · Replies 21 ·
Replies
21
Views
4K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Reason out the cross product (for the moment): a skew symmetric form
  • · Replies 14 ·
Replies
14
Views
4K
Misc. Yarn cross-section and path length
  • · Replies 3 ·
Replies
3
Views
1K
High School Confusion about the angle between two vectors in a cross product
  • · Replies 7 ·
Replies
7
Views
3K
Understanding the Dot Product and Cross Product in Vector Calculations
  • · Replies 6 ·
Replies
6
Views
2K
High School A "no hands" rule for the cross product (requires literacy)
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Cyclic rotation of the cross product involving derivation
  • · Replies 12 ·
Replies
12
Views
2K
Obtain an equation of the plane in the form ##px+qy+rz=d##
  • · Replies 5 ·
Replies
5
Views
1K