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Linear and Abstract Algebra Forum

Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.

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Who First Utilized Rigorous Proofs in Mathematics?

Apr 29, 2011 · Replies 4 · May 3, 2011

Replies: 4

Views: 3K

Clifford Algebras: Finding Matrix Representations Cl(0,n)

Apr 26, 2011 · Replies 2 · May 2, 2011

Replies: 2

Views: 3K

Hermitian operators without considering them as Matrices

Apr 30, 2011 · Replies 1 · May 2, 2011

Replies: 1

Views: 3K

Products of disjoint cycles. Explanation please.

May 2, 2011 · Replies 5 · May 2, 2011

Replies: 5

Views: 8K

Pattern to indexes of deletions in a seive.

May 1, 2011 · Replies 2 · May 2, 2011

Replies: 2

Views: 2K

Proving extrema using taylor series and Hessian Matrix

Apr 30, 2011 · Replies 4 · May 1, 2011

Replies: 4

Views: 4K

Matrix equation - numeric solving

Apr 30, 2011 · Replies 2 · May 1, 2011

Replies: 2

Views: 2K

Garrity's Formula: Ordering Covariant Alternating Tensors

Apr 29, 2011 · Replies 1 · Apr 30, 2011

Replies: 1

Views: 2K

Proving the Even Rank of Skew Symmetric Matrices: Induction and Other Methods

Apr 30, 2011 · Replies 1 · Apr 30, 2011

Replies: 1

Views: 4K

Jordan Normal Form physical applications

Apr 29, 2011 · Replies 2 · Apr 30, 2011

Replies: 2

Views: 4K

Countable Sets: Cantor's Theorem & Galileo's Paradox

Apr 29, 2011 · Replies 1 · Apr 29, 2011

Replies: 1

Views: 2K

Is a Matrix Zero if Its Inner Product with All Vector Combinations Equals Zero?

Apr 29, 2011 · Replies 2 · Apr 29, 2011

Replies: 2

Views: 2K

Rank of AB: How nxn Matrices A & B Determine Rank

Apr 28, 2011 · Replies 2 · Apr 29, 2011

Replies: 2

Views: 3K

How can the existence of the tensor product be proven in Federer's construction?

Apr 29, 2011 · Replies 2 · Apr 29, 2011

Replies: 2

Views: 2K

Subgroup Order in Groups of Divisible Orders: Proof or Counterexamples?

Apr 29, 2011 · Replies 1 · Apr 29, 2011

Replies: 1

Views: 2K

Groups and orthogonal matrices question

Apr 27, 2011 · Replies 7 · Apr 28, 2011

Replies: 7

Views: 3K

Show that if all the row sums of a matrix A belong to C (nxm) are

Apr 28, 2011 · Replies 2 · Apr 28, 2011

Replies: 2

Views: 2K

Cleaning up vocabulary and concepts

Apr 27, 2011 · Replies 2 · Apr 28, 2011

Replies: 2

Views: 2K

Generalization of Lines, Planes (Finite Fields)

Apr 27, 2011 · Replies 1 · Apr 27, 2011

Replies: 1

Views: 1K

Finding eigenvalues of a 3 x 3 matrix

Apr 26, 2011 · Replies 2 · Apr 26, 2011

Replies: 2

Views: 5K

Is the Product of A and An in a Cyclic Group of Order n Outside the Group?

Apr 25, 2011 · Replies 3 · Apr 26, 2011

Replies: 3

Views: 2K

(n-1)-dimensional subspace is the null space of a linear functional

Apr 26, 2011 · Replies 2 · Apr 26, 2011

Replies: 2

Views: 4K

Is \(\mathbb{Q}(\sqrt{5})\) a Unique Factorization Domain?

Apr 25, 2011 · Replies 3 · Apr 26, 2011

Replies: 3

Views: 3K

Chinese Remainder Theorem: A Powerful Tool in Number Theory

Apr 6, 2006 · Replies 5 · Apr 24, 2011

Replies: 5

Views: 7K

Normal Derivative at Boundary Surface S Explained

Apr 22, 2011 · Replies 9 · Apr 24, 2011

Replies: 9

Views: 23K

Fonction smaller than iterated logs, but not constant

Mar 13, 2011 · Replies 5 · Apr 24, 2011

Replies: 5

Views: 4K

How to show something is a subspace

Apr 23, 2011 · Replies 4 · Apr 24, 2011

Replies: 4

Views: 7K

Lattices in nilpotent Lie groups

Sep 22, 2008 · Replies 1 · Apr 24, 2011

Replies: 1

Views: 2K

Linear Independence/Dependence of Vectors

Sep 29, 2008 · Replies 6 · Apr 23, 2011

Replies: 6

Views: 12K

Relationship Between Symplectic Group and Orthogonal Group

Apr 20, 2011 · Replies 2 · Apr 23, 2011

Replies: 2

Views: 3K

Is U + U' a subspace if U and U' are contained in W?

Apr 20, 2011 · Replies 5 · Apr 23, 2011

Replies: 5

Views: 3K

How to convert polynomial to matrix?

Apr 18, 2004 · Replies 3 · Apr 22, 2011

Replies: 3

Views: 43K

Are Matrices with the Same Eigenvalues Always Similar?

Apr 15, 2011 · Replies 16 · Apr 22, 2011

Replies: 16

Views: 21K

Proving Gauss's Lemma Extension in Polynomial Factoring

Apr 21, 2011 · Replies 1 · Apr 22, 2011

Replies: 1

Views: 3K

Left- and Right- Kernels of Bilinear maps B:VxV->K for V.Spaces

Apr 21, 2011 · Replies 1 · Apr 22, 2011

Replies: 1

Views: 4K

Q: Notation for Differentiable Functions

Apr 21, 2011 · Replies 2 · Apr 21, 2011

Replies: 2

Views: 2K

Vectors with different coordinate systems

Apr 20, 2011 · Replies 2 · Apr 21, 2011

Replies: 2

Views: 3K

Can someone explain the Lie algebra concept to me?

Apr 21, 2011 · Replies 1 · Apr 21, 2011

Replies: 1

Views: 2K

Finding the canonical form of a quadratic form.

Apr 19, 2011 · Replies 3 · Apr 21, 2011

Replies: 3

Views: 7K

Complex Hilbert Space as a Symplectic Space?

Apr 20, 2011 · Replies 2 · Apr 20, 2011

Replies: 2

Views: 3K

Is R a Subring of M2(Z)?

Apr 20, 2011 · Replies 4 · Apr 20, 2011

Replies: 4

Views: 4K

What Are Homology and Graded Groups in Mathematics?

Oct 15, 2005 · Replies 8 · Apr 20, 2011

Replies: 8

Views: 5K

How do you find the basis for the spanning set which contains matrices?

Apr 19, 2011 · Replies 5 · Apr 20, 2011

Replies: 5

Views: 5K

What Are the Best Online Resources for Learning Abstract Algebra?

Apr 8, 2011 · Replies 2 · Apr 20, 2011

Replies: 2

Views: 3K

Listing the elements of a symmetry group of a frieze pattern

Apr 16, 2011 · Replies 1 · Apr 18, 2011

Replies: 1

Views: 3K

Differnece between the Kernel and the Nullspace?

May 3, 2010 · Replies 17 · Apr 18, 2011

Replies: 17

Views: 18K

How can a vector be multiplied by itself ?

Apr 16, 2011 · Replies 7 · Apr 17, 2011

Replies: 7

Views: 6K

Discover the Transcendental Nature of E+pi at AMS Meetings

Apr 6, 2011 · Replies 9 · Apr 17, 2011

Replies: 9

Views: 5K

Prove an Infinite Series is Irrational

Mar 13, 2011 · Replies 21 · Apr 17, 2011

Replies: 21

Views: 11K

Permutation Group: Understanding Elementary Permutations

Apr 15, 2011 · Replies 29 · Apr 16, 2011

Replies: 29

Views: 4K

Derivative of determinant wrt matrix

Apr 5, 2011 · Replies 3 · Apr 16, 2011

Replies: 3

Views: 7K

Why is the Integer Group Z Considered Cyclic?

Apr 16, 2011 · Replies 1 · Apr 16, 2011

Replies: 1

Views: 9K

Quotient Ring of a Polynomial Ring

Apr 14, 2011 · Replies 1 · Apr 15, 2011

Replies: 1

Views: 3K

Usefulness of Basis for a Vector Space, General?

Apr 13, 2011 · Replies 8 · Apr 15, 2011

Replies: 8

Views: 3K

Mobius transformation (isomorphism)

Apr 13, 2011 · Replies 4 · Apr 15, 2011

Replies: 4

Views: 4K

Solution to a linear equation of matrices

Apr 6, 2011 · Replies 5 · Apr 14, 2011

Replies: 5

Views: 3K

Column Space Basis: Why Does Row Reduction Work?

Dec 4, 2010 · Replies 10 · Apr 14, 2011

Replies: 10

Views: 9K

Suppose I get the eigenvalues of A, which are

Apr 14, 2011 · Replies 2 · Apr 14, 2011

Replies: 2

Views: 1K

Proof for cross product (please)

Mar 25, 2009 · Replies 17 · Apr 14, 2011

Replies: 17

Views: 11K

Evaluating Continued Fraction: \langle 1, 2, 1, 2, \ldots \rangle

Apr 13, 2011 · Replies 3 · Apr 13, 2011

Replies: 3

Views: 2K

Nonlinear Least Squares Minimization

Apr 13, 2011 · Replies 1 · Apr 13, 2011

Replies: 1

Views: 2K

Sequence what is the formula? 2 0 2 0 3 3 2 4

Apr 12, 2011 · Replies 6 · Apr 13, 2011

Replies: 6

Views: 3K

I writing a mathematica function.

Apr 9, 2011 · Replies 5 · Apr 13, 2011

Replies: 5

Views: 3K

What are the Properties of (0,1)-Matrices with Constant Row Sum 3?

Apr 1, 2011 · Replies 20 · Apr 13, 2011

Replies: 20

Views: 6K

Optimizing Matrix Inversions: Tips for Faster Calculations

Apr 9, 2011 · Replies 6 · Apr 12, 2011

Replies: 6

Views: 15K

Sum of Numbers with distinct digiits?

Apr 6, 2011 · Replies 16 · Apr 12, 2011

Replies: 16

Views: 7K

Proving Completeness Relations in Orthonormal Bases | Quantum Mechanics

Apr 11, 2011 · Replies 4 · Apr 12, 2011

Replies: 4

Views: 8K

Is There a Rational Point Not Equidistant from Any Two Lattice Points?

Apr 11, 2011 · Replies 1 · Apr 11, 2011

Replies: 1

Views: 4K

Showing two matrices are not unitarily similar

Apr 10, 2011 · Replies 4 · Apr 11, 2011

Replies: 4

Views: 4K

Order of Eigenvectors in Diagonalization

Apr 11, 2011 · Replies 1 · Apr 11, 2011

Replies: 1

Views: 3K

Finding an Orthogonal Polynomial to x^2-1/2 on L2[0,1]

Apr 10, 2011 · Replies 2 · Apr 11, 2011

Replies: 2

Views: 3K

Modulus Predictions for Binomial Expansion Coefficients?

Apr 10, 2011 · Replies 4 · Apr 10, 2011

Replies: 4

Views: 3K

Spectral Radius Inequality for Matrix Products

Apr 10, 2011 · Replies 1 · Apr 10, 2011

Replies: 1

Views: 2K

Natural isomorphisms between dual spaces

Apr 8, 2011 · Replies 6 · Apr 10, 2011

Replies: 6

Views: 4K

Find P2 on Plane Given P1 & Dist. 3 Units

Apr 9, 2011 · Replies 3 · Apr 9, 2011

Replies: 3

Views: 2K

Writing numbers in statistical way?

Apr 8, 2011 · Replies 3 · Apr 9, 2011

Replies: 3

Views: 2K

Does Every Field Have a Subfield Isomorphic to Q or Z mod p?

Apr 9, 2011 · Replies 3 · Apr 9, 2011

Replies: 3

Views: 2K

Listen to Ethereal Primal Music of Pi

Apr 3, 2011 · Replies 2 · Apr 9, 2011

Replies: 2

Views: 2K

Adjoint Functors: Explaining What They ARE

Apr 6, 2011 · Replies 3 · Apr 9, 2011

Replies: 3

Views: 3K

Infinite Semi-Pronic Prime Series Appears to Converge

Mar 30, 2011 · Replies 3 · Apr 8, 2011

Replies: 3

Views: 4K

I am trying to relate eigenvalues with singular values. In particular,

Apr 7, 2011 · Replies 2 · Apr 8, 2011

Replies: 2

Views: 2K

Perfect Numbers and their reciprocals.

Apr 7, 2011 · Replies 2 · Apr 8, 2011

Replies: 2

Views: 3K

Prime & Maximal Ideals of $\mathbb Z_7$ & $\mathbb Z_3 \times \mathbb Z_5$

Apr 7, 2011 · Replies 1 · Apr 7, 2011

Replies: 1

Views: 4K

How are multiplication tables for fields created?

Apr 7, 2011 · Replies 1 · Apr 7, 2011

Replies: 1

Views: 4K

What does a three-dimensional matrix look like?

Apr 5, 2011 · Replies 20 · Apr 7, 2011

Replies: 20

Views: 11K

Could somebody help motivate linear algebra for me?

Apr 5, 2011 · Replies 7 · Apr 7, 2011

Replies: 7

Views: 4K

Cholesky for complex *symmetric*

Apr 6, 2011 · Replies 3 · Apr 7, 2011

Replies: 3

Views: 4K

Help Interpeting Mathematica Result

Apr 4, 2011 · Replies 4 · Apr 6, 2011

Replies: 4

Views: 2K

Totient function and distinct primes.

Apr 5, 2011 · Replies 7 · Apr 6, 2011

Replies: 7

Views: 5K

The Mysterious Nature of Prime Numbers in Science

Jun 30, 2008 · Replies 24 · Apr 6, 2011

Replies: 24

Views: 7K

Finding symmetries both geometrically and analytically. PLEASE HELP

Apr 1, 2011 · Replies 4 · Apr 6, 2011

Replies: 4

Views: 2K

Is a Direct Sum of Rings Composed of Elements from Each Original Ring?

Apr 14, 2010 · Replies 2 · Apr 6, 2011

Replies: 2

Views: 3K

General rule for a confusing series

Apr 3, 2011 · Replies 2 · Apr 6, 2011

Replies: 2

Views: 2K

Does a Perfect Square Lie Within these 10 Integers?

Mar 28, 2011 · Replies 2 · Apr 5, 2011

Replies: 2

Views: 2K

Solve Line Intersection Word Problem: Car A vs Car B

Apr 4, 2011 · Replies 9 · Apr 5, 2011

Replies: 9

Views: 2K

Conjectures by Legendre and Brocard made stronger.

Apr 4, 2011 · Replies 2 · Apr 5, 2011

Replies: 2

Views: 3K

How Can I Linearize the Complex Function z = (2+i)/(i(-3+4i))?

Apr 5, 2011 · Replies 3 · Apr 5, 2011

Replies: 3

Views: 2K

Can I Find an Expression Relating x to x1 and x2 while Decomposing Operator A?

Apr 4, 2011 · Replies 1 · Apr 5, 2011

Replies: 1

Views: 2K

The Commutator in Group Theory vs QM

Apr 2, 2011 · Replies 6 · Apr 5, 2011

Replies: 6

Views: 3K

Diagonalizability and Invertibility

Mar 26, 2009 · Replies 9 · Apr 4, 2011

Replies: 9

Views: 20K

Linear and Abstract Algebra

Linear and abstract algebra are branches of mathematics that deal with algebraic structures and their properties.

Linear algebra primarily focuses on vector spaces, linear transformations, and systems of linear equations. It provides essential tools for understanding geometric concepts, solving linear equations, and working with matrices. Abstract algebra, on the other hand, is a more generalized study that investigates algebraic structures such as groups, rings, and fields. It delves into the properties and relationships of algebraic systems, aiming to identify common structures and abstract patterns.

Both linear and abstract algebra are foundational areas of mathematics with applications spanning diverse fields, from physics and computer science to cryptography and optimization.

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