Properties of Cross Product: Algebraic Aspects

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Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

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Covers alternating and symmetric multilinear forms in vector spaces over a field.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.

Explores the special linear group, matrix properties, and determinant theorems.

Explores permutations, signature, and alternating multilinear forms in vectors.

Provides an overview of algebraic manipulations involving indices and tensors in continuum mechanics.

Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.