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Does anyone have any good refreshers/tutorials for exterior algebra? I need to reacquaint myself with differentials and wedge products specifically. Thanks.
Exterior algebra is a branch of mathematics that deals with the algebraic structures called exterior algebras, which are used to study geometric properties of vector spaces and their transformations.
In exterior algebra, differentials are used to represent the derivative of a multivariable function. They are represented by the wedge product of vectors and are used to calculate the change in a function with respect to each variable.
The wedge product is an operation in exterior algebra that combines two vectors to create a new vector with properties that reflect the geometrical relationship between the two original vectors. It is used to represent the cross product in higher-dimensional spaces.
Exterior algebra is used in physics to study geometric properties of physical systems, such as those in electromagnetism and general relativity. It is also used in quantum mechanics to represent the spin of particles.
Exterior algebra has many applications in mathematics, physics, and engineering. Some examples include differential geometry, robotics, computer graphics, and computer vision.