Linear and Abstract Algebra Forum

Post thread
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.
Fundamental Theorem of Arithmetic Problem
  • · Replies 14 ·
Replies
14
Views
5K
Isomorphism (Fraleigh 7th: Section 5)
  • · Replies 8 ·
Replies
8
Views
5K
Confusing about linearity and nonlinearity
  • · Replies 2 ·
Replies
2
Views
2K
Uniqueness Theorem for homogenous linear ODEs
  • · Replies 5 ·
Replies
5
Views
6K
Non-uniform bi-linear interpolation
  • · Replies 2 ·
Replies
2
Views
13K
I dont get the point of pseudovectors
  • · Replies 7 ·
Replies
7
Views
8K
LU Decomposition: Calculating Determinant of Square Matrix (Example Included)
  • · Replies 1 ·
Replies
1
Views
10K
How to Diagonalize a 9x9 Matrix with Unitary Vectors?
  • · Replies 6 ·
Replies
6
Views
2K
Null matrix and invertible matrix
  • · Replies 1 ·
Replies
1
Views
3K
Geometrical interpretation of dot product (trying to prove)
  • · Replies 17 ·
Replies
17
Views
8K
Innner products and basis representation
  • · Replies 5 ·
Replies
5
Views
2K
How can I compute r from: c = g^m * r^N mod N^2
  • · Replies 5 ·
Replies
5
Views
3K
Eigenvalues and eigenvectors of this matrix
  • · Replies 1 ·
Replies
1
Views
3K
Why is Ax in col(A) if (A^T)Ax=0
  • · Replies 2 ·
Replies
2
Views
2K
Reduce P = A(ATA)-1AT to P = BBT
  • · Replies 1 ·
Replies
1
Views
2K
What is the meaning of the subscript in the polygamma function?
  • · Replies 1 ·
Replies
1
Views
2K
What Is a Lie Group Without an Identity Matrix Called?
  • · Replies 3 ·
Replies
3
Views
2K
Projection Matrix: P=A(ATA)^-1AT & P=BBT
  • · Replies 2 ·
Replies
2
Views
3K
How to find two endpoints of a line?
  • · Replies 5 ·
Replies
5
Views
4K
What Are the Key Properties of Hyperreal Numbers?
  • · Replies 10 ·
Replies
10
Views
4K
Transformation to flip handedness of a 4-vector
  • · Replies 2 ·
Replies
2
Views
2K
Column Space and Pivot Columns in Reduced Matrices
  • · Replies 1 ·
Replies
1
Views
5K
Simple Proof Check - Number Theory
  • · Replies 4 ·
Replies
4
Views
3K
Question about the definition of a vector space
  • · Replies 9 ·
Replies
9
Views
3K
Is it possible to determine if a number is a perfect square in different bases?
  • · Replies 5 ·
Replies
5
Views
4K
Why Are SU(3) Generators Traceless and Limited to Two Diagonal Matrices?
  • · Replies 6 ·
Replies
6
Views
3K
How can I find an endorser for my prime number papers on ArXiv?
  • · Replies 3 ·
Replies
3
Views
4K
How can a column represent a vector in linear algebra?
  • · Replies 4 ·
Replies
4
Views
2K
Proving the Finiteness of Fermat Primes
  • · Replies 27 ·
Replies
27
Views
6K
Is the only difference between functions just a change of basis?
  • · Replies 1 ·
Replies
1
Views
5K
Is There Always a Prime Number Between n and n! for n>2?
  • · Replies 8 ·
Replies
8
Views
8K
Can We Obtain the Form of L from Z(u)?
  • · Replies 1 ·
Replies
1
Views
2K
I came across this Proposition in my book, and I know it's something
  • · Replies 1 ·
Replies
1
Views
2K
How do i get the point of intersection of a line and a circle?
  • · Replies 3 ·
Replies
3
Views
12K
Solving Linear Equations: Expanding Brackets, Subbing Values
  • · Replies 8 ·
Replies
8
Views
2K
Irreducible Representations of so(4,C)
  • · Replies 2 ·
Replies
2
Views
6K
Numerical algorithms for finding an eigenvector
  • · Replies 4 ·
Replies
4
Views
4K
Is a symmetric matrice allways nonsingular?
  • · Replies 1 ·
Replies
1
Views
2K
Proving Real Numbers, Pythagorean Triples & Squares
  • · Replies 14 ·
Replies
14
Views
4K
Matrix determinant operator commutative?
  • · Replies 3 ·
Replies
3
Views
10K
Proving Self-Adjointness in Finite-Dimensional Vector Spaces with Inner Products
  • · Replies 8 ·
Replies
8
Views
3K
Proof of Schwarz Inequality: Axioms & Complex Numbers
  • · Replies 6 ·
Replies
6
Views
5K
Clifford Algebra: Representing Vectors & Projecting to Euclidean
  • · Replies 4 ·
Replies
4
Views
3K
Group (Associativity of Binary Operators)
  • · Replies 1 ·
Replies
1
Views
2K
Why Is QQ^T Singular for a Matrix with Orthonormal Columns?
  • · Replies 5 ·
Replies
5
Views
5K
Coprime pythagorean quadruples or higher tuples?
  • · Replies 4 ·
Replies
4
Views
6K
Show every group of order 77 has elements of order 7 and 11
  • · Replies 8 ·
Replies
8
Views
11K
Legendre and Riemann: A Conjecture Comparison
  • · Replies 6 ·
Replies
6
Views
3K
Relating to Duality in Vector Spaces
  • · Replies 7 ·
Replies
7
Views
3K
Number Theory integer roots Problem
  • · Replies 16 ·
Replies
16
Views
6K
Intermediate Ratio: Proof & Name
  • · Replies 1 ·
Replies
1
Views
4K
Website title: Finding Rotation Matrices for Arbitrary Angle Rotations in R^3
  • · Replies 4 ·
Replies
4
Views
3K
What is a Linear Manifold and How Does it Differ from a Subspace?
  • · Replies 2 ·
Replies
2
Views
2K
Proving Eigenspace Correspondence for Similar Matrices
  • · Replies 2 ·
Replies
2
Views
6K
F4 algorithm for calculating Groebner bases
  • · Replies 6 ·
Replies
6
Views
5K
What is the Probability of Factoring Random Monic Polynomials?
  • · Replies 1 ·
Replies
1
Views
3K
Transformation matrix on tensors
  • · Replies 2 ·
Replies
2
Views
2K
Describing the Sylow 2-subgroups of S5
  • · Replies 1 ·
Replies
1
Views
8K
Proof of A^(de) = a mod n for All Integers a
  • · Replies 1 ·
Replies
1
Views
2K
Is the Sum of Digits Always Nine?
  • · Replies 8 ·
Replies
8
Views
22K
A non-trivial infinity of zeroes with real part one-half
  • · Replies 15 ·
Replies
15
Views
5K
A matrix is diagonalizable when algebraic and geometric multiplicities are equal
  • · Replies 2 ·
Replies
2
Views
8K
How Can I Solve This Unique Weight Balancing Problem Using Balanced Ternary?
  • · Replies 2 ·
Replies
2
Views
4K
Conjugate Homogeneity for Self-Adjoint Operators: Proof and Explanation
  • · Replies 3 ·
Replies
3
Views
3K
Is the sequence finite for different values of u in the logarithmic series?
  • · Replies 2 ·
Replies
2
Views
2K
Understanding and Expanding the 2nd Chebyshev Function: Calculation Help
  • · Replies 1 ·
Replies
1
Views
2K
Is Legendre's Conjecture on Primes Between n² and (n+1)² Fully Resolved?
  • · Replies 3 ·
Replies
3
Views
5K
A matrix is diagonalizable when algebraic and geometric multiplicities are equal
  • · Replies 2 ·
Replies
2
Views
3K
Is a Matrix Symmetric if Row Space Equals Column Space?
  • · Replies 3 ·
Replies
3
Views
3K
Unimodular Matrices: Geometric Interpretation
  • · Replies 4 ·
Replies
4
Views
2K
How Can x*0=0 Be Proven Without Using m(-1)=-m?
  • · Replies 3 ·
Replies
3
Views
9K
Question about Gram-Schmidt orthogonalization
  • · Replies 2 ·
Replies
2
Views
3K
Basis for the set of all cts fns?
  • · Replies 15 ·
Replies
15
Views
4K
Understanding Pressure Equations in Linear and Abstract Algebra
  • · Replies 4 ·
Replies
4
Views
3K
Constructing an irreducible polynomial in Z_{p^(m+1)}
  • · Replies 1 ·
Replies
1
Views
2K
Revisiting Algebra Basics: 4ax + 2ay = 2a(2x + y)
  • · Replies 2 ·
Replies
2
Views
2K
Index Conventions in Linear Algebra & Apps: David Griffel
  • · Replies 2 ·
Replies
2
Views
3K
Adjoint transformation (inverse)
  • · Replies 4 ·
Replies
4
Views
4K
What are the two definitions of gamma function and how are they related?
  • · Replies 2 ·
Replies
2
Views
2K
Are Eigenvalues of a Non-Hermitian Matrix Real?
  • · Replies 2 ·
Replies
2
Views
3K
Can the Gamma Function Summation Be Simplified for 0<Re(s)<1?
  • · Replies 1 ·
Replies
1
Views
3K
Proving Subspace of a Matrix in R2
  • · Replies 8 ·
Replies
8
Views
3K
Proof Question: Invariance of U and U⊥ under T and T∗ for V subspace"
  • · Replies 3 ·
Replies
3
Views
2K
What is the significance of zero in mathematics and philosophy?
  • · Replies 13 ·
Replies
13
Views
14K
Are half of all natural numbers even?
  • · Replies 9 ·
Replies
9
Views
4K
Point or Vector? What's the difference?
  • · Replies 35 ·
2
Replies
35
Views
56K
Fastest way you have found to multiply two numbers in your head?
  • · Replies 7 ·
Replies
7
Views
6K
Vandermonde Matrix, Polynomial Interpolation & Orthogonal Basis
  • · Replies 1 ·
Replies
1
Views
4K
Another question about projections.
  • · Replies 4 ·
Replies
4
Views
2K
How could I change an equation to look the same as it did with inverted axes?
  • · Replies 1 ·
Replies
1
Views
2K
X,Y and Z operators of some algebra
  • · Replies 1 ·
Replies
1
Views
2K
Is the Solution Set of Ax=b a Subspace of R^n?
  • · Replies 1 ·
Replies
1
Views
2K
Can Recursive Flip-Trees Be Defined More Elegantly?
  • · Replies 3 ·
Replies
3
Views
7K
What Are the Properties of an Endomorphism f That Satisfies x*f(x)=k?
  • · Replies 21 ·
Replies
21
Views
3K
Subgroup wth morphism into itself
  • · Replies 2 ·
Replies
2
Views
1K
Sequel for my proof for Riemann's hypothesis
  • · Replies 4 ·
Replies
4
Views
3K
Accurate Proof and varification for Riemann Hypothesis
  • · Replies 1 ·
Replies
1
Views
3K
Convolution Inverse: Family of Functions Explained
  • · Replies 7 ·
Replies
7
Views
26K
Why Does This Polylogarithm Identity Have No Restrictions?
  • · Replies 1 ·
Replies
1
Views
2K
Question about orthogonal projections.
  • · Replies 4 ·
Replies
4
Views
2K