Algebra
Anki flash cards loosely based on parts of Algebra: Chapter 0 by Paolo Aluffi.
- Transpose characterized
- Preloaded dot product
- Covariance of random vector linearly transformed
- Singular value decomposition
- Viewing matrices through SVD
- Spectral Theorem
- Eigenvector decomposition. Equivalent forms.
- Markov matrices and their eigenvectors. An NZ-AU immigration example.
- A = LU decomposition when A is symmetric
- Determinant from pivots
- LU decomposition
- Inverse of triangular matrix
- Effect of add-identity to eigenvectors
- Reduced row echelon form
- Eigenvalues of a triangular matrix
- Diagonally dominant
- Product of eigenvalues and sum of eigenvalues
- Eigenvectors of projection and reflection matricies
- Projection matrix
- Affine function
- Tim Gowers on "well-defined"
- Prime and maximal ideals
- Two new rings from polynomial ring quotients
- Two new rings from polynomial ring quotients
- Group isomorphism: quotient of R[x] ≅ direct sum of R
- Rings. Uniqueness of polynomial division.
- Rings. Third isomorphism theorem, an example.
- Rings. Third isomorphism theorem.
-
Euler's
- Subgroups of the general linear group
- Groups. Monomorphism equivalents.
- Subgroups of cyclic groups
- Property of polynomial rings
- Groups. Group action.
- Rings. Zero-divisors.
- Polynomial rings
- Ring. Definition.
- Rings. Additional structure.
- Ring. As a group of group endomorphisms.
- The uniqueness of the zero ring
- Groups. Some properties of order.
- Groups. Lagrange's theorem.
- Canonical decomposition in the Grp category
- Groups. Kernel.
- Normal subgroup
- Quotient group. From equivalence condition.
- Quotient groups. From Cosets.
- Cosets
- Subgroups. Definition.
- Subgroups. Propositions.
- Group homomorphism
- Group homomorphisms and order
- Group Isomorphism
- Groups. All orders divides order of maximal element
- Isomorphisms of cyclic group products
- The set products satisfy the coproduct property in the Abelian category.
- Category of Groups
- Groups. Group datum.
- Groups. Some properties of order.
- Groups. Order for commutative product.
- Groups. Order.
- Groups. 3 basic lemmas.
- Group. Definition.
- Initial and final objects
- Universal properties. Quotient.
- Monomorphisms and epimorphisms
- Endomorphisms and automorphisms
- Isomorphism
- Slice category
- Category Theory. Essence of associative composition.
- Category. Definition.
- Canonical decomposition
- Identity, inclusion and restriction
- Injectivity and surjectivity
- Equivalence relations
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