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.
How can I find a solution valid for all cases?
  • · Replies 5 ·
Replies
5
Views
3K
Find Basis for Subspace of R^4 Spanned by Vectors
  • · Replies 6 ·
Replies
6
Views
20K
Reducing the operation by using the modulo
  • · Replies 15 ·
Replies
15
Views
7K
Primes as Energy levels (eigenvalues of a certain operator)
  • · Replies 5 ·
Replies
5
Views
6K
What is the relationship between rank and submatrices in a nonzero matrix?
  • · Replies 2 ·
Replies
2
Views
8K
Projections onto a plane and parallel to a vector
  • · Replies 1 ·
Replies
1
Views
4K
Sum A+cB of invertible matrices noninvertible?
  • · Replies 2 ·
Replies
2
Views
3K
Inverse matrix with whole numbers
  • · Replies 10 ·
Replies
10
Views
9K
What is the difference between Field and Set ?
  • · Replies 12 ·
Replies
12
Views
13K
Discriminant of a quadratic equation in 2 variables
  • · Replies 3 ·
Replies
3
Views
11K
Question about finding dimensions
  • · Replies 4 ·
Replies
4
Views
3K
Combine upper, lower, and diagonal matrix?
  • · Replies 1 ·
Replies
1
Views
4K
Characterizing Affine Independence
  • · Replies 2 ·
Replies
2
Views
5K
Understanding the Relationship Between Exterior and Cross Products
  • · Replies 7 ·
Replies
7
Views
3K
Norms and Units of an Integral Domain
  • · Replies 1 ·
Replies
1
Views
3K
How to Prove a Matrix is Diagonal?
  • · Replies 6 ·
Replies
6
Views
7K
Tensor product and infinite dimensional vector space
  • · Replies 1 ·
Replies
1
Views
4K
What does this statement even mean?
  • · Replies 14 ·
Replies
14
Views
3K
Is the Units Group of Z Modulo 34 Cyclic?
  • · Replies 2 ·
Replies
2
Views
3K
Determine whether the function is a linear transformation (Attempt inside)
  • · Replies 1 ·
Replies
1
Views
4K
What Other Iterative Methods Can Be Used If A is Not Positive Definite?
  • · Replies 1 ·
Replies
1
Views
2K
When to Solve for dimH vs. Column Space or Null Space?
  • · Replies 5 ·
Replies
5
Views
3K
How Do You Find Non-Parallel Vectors in a Plane Defined by an Equation?
  • · Replies 1 ·
Replies
1
Views
2K
Are these vector spaces isomorphs?
  • · Replies 1 ·
Replies
1
Views
2K
Variable power as an axis, nonsense? please comment
  • · Replies 4 ·
Replies
4
Views
3K
How to Prove a Group with 2n-1 Subgroups is Trivial or Isomorphic to Z2?
  • · Replies 11 ·
Replies
11
Views
6K
Is there a formula for calculating partitions with restrictions?
  • · Replies 5 ·
Replies
5
Views
4K
(Q,+, .) is a commutative ring : confusion
  • · Replies 12 ·
Replies
12
Views
3K
Trouble understanding spans of vector spaces
  • · Replies 5 ·
Replies
5
Views
6K
Why is this always the case A=[itex]\begin{array}{cc}1 & 6
  • · Replies 2 ·
Replies
2
Views
2K
What are the prerequisites for learning Linear Algebra?
  • · Replies 6 ·
Replies
6
Views
31K
Galois Theory questions: Homomorphisms
  • · Replies 1 ·
Replies
1
Views
3K
Spanning sets, eigenvalues, eigenvectors etc .
  • · Replies 3 ·
Replies
3
Views
5K
Solving Ax=b; when to use LU decomposition?
  • · Replies 8 ·
Replies
8
Views
12K
Inverting a function? f(y) instead of f(x)
  • · Replies 2 ·
Replies
2
Views
3K
Shrinking down a^b mod m when b is huge and a is irrational?
  • · Replies 8 ·
Replies
8
Views
4K
Are H Union K and Z(g) Subgroups in Group Theory?
  • · Replies 1 ·
Replies
1
Views
4K
How Many Homomorphisms Can Be Calculated Between Different Fields?
  • · Replies 2 ·
Replies
2
Views
3K
How do I check if a 1x1 matrix is diagonal, lower/upper triangular?
  • · Replies 2 ·
Replies
2
Views
10K
Zp[x]/(x^2 + 1) is a field iff p is a prime p ≠ 1 (mod 4)
  • · Replies 12 ·
Replies
12
Views
10K
How Are Rational and Irrational Numbers Distributed Along the Real Line?
  • · Replies 9 ·
Replies
9
Views
7K
What can commute with a diagonal matrix?
  • · Replies 5 ·
Replies
5
Views
22K
Composition of functions and operator algebra.
  • · Replies 4 ·
Replies
4
Views
3K
Matrix of a Linear Transformation (Abstract)
  • · Replies 1 ·
Replies
1
Views
3K
Modular arithmetic question about functions
  • · Replies 2 ·
Replies
2
Views
2K
How can I visualize the plane y=z?
  • · Replies 3 ·
Replies
3
Views
2K
Understanding Cosets and Subspaces in Linear Algebra
  • · Replies 3 ·
Replies
3
Views
7K
Is S4 a Subset of S5?
  • · Replies 2 ·
Replies
2
Views
4K
How does the identity Ln(detA)=Tr(lnJ) hold true?
  • · Replies 9 ·
Replies
9
Views
25K
Find a prime divisor of 1111 (13 1's)
  • · Replies 2 ·
Replies
2
Views
2K
Simple question regarding polynomials
  • · Replies 2 ·
Replies
2
Views
2K
Collatz Conjecture: Plotting Integer Steps with Joe
  • · Replies 9 ·
Replies
9
Views
5K
Understand Irreducibility in Zp: What is Zp^x? Order of Elements in Zp
  • · Replies 3 ·
Replies
3
Views
4K
Exponential of jordan form involving distinct eigenvalues
  • · Replies 4 ·
Replies
4
Views
8K
How to Find Convergents of a Continued Fraction?
  • · Replies 1 ·
Replies
1
Views
4K
Hello,The pseudoinverse formula for a matrix A is given by:P =
  • · Replies 1 ·
Replies
1
Views
2K
Is the Riemann Hypothesis Equivalent to S=2Z?
  • · Replies 7 ·
Replies
7
Views
4K
Inner product of vectors and covectors
  • · Replies 8 ·
Replies
8
Views
6K
Constraining the element-wise magnitudes of a matrix
  • · Replies 2 ·
Replies
2
Views
3K
Group Action of S3 on a set of ordered pairs
  • · Replies 4 ·
Replies
4
Views
7K
What is the Value of (p+q-2t) and (p^2+q^2-2t^2) in an Equation with Degree 3?
  • · Replies 2 ·
Replies
2
Views
2K
Tricky complex square matrix problem
  • · Replies 7 ·
Replies
7
Views
4K
Does anyone know the name of this type of map
  • · Replies 1 ·
Replies
1
Views
2K
Left group actions involving SO(3) and the 2-sphere
  • · Replies 2 ·
Replies
2
Views
5K
Real Numbers vs Extended Real Numbers
  • · Replies 5 ·
Replies
5
Views
5K
Factor Groups: Conjugation & 2 Conjugates
  • · Replies 2 ·
Replies
2
Views
2K
Integer values of this expression
  • · Replies 4 ·
Replies
4
Views
3K
Abstract Algebra - Cyclic groups
  • · Replies 3 ·
Replies
3
Views
5K
What topics from linear algebra do I need to study tensors?
  • · Replies 19 ·
Replies
19
Views
5K
Why is not angle considered as vector?
  • · Replies 10 ·
Replies
10
Views
3K
Simple summation, difficult inference. (game theory)
  • · Replies 2 ·
Replies
2
Views
3K
Principal ideals of rings without unity
  • · Replies 5 ·
Replies
5
Views
5K
Power Series Expansion of Dedekind Eta Function: How to Expand η(τ)/η(3τ)?
  • · Replies 2 ·
Replies
2
Views
3K
Linear Algebra: Can't make sense of it
  • · Replies 14 ·
Replies
14
Views
6K
Riemann zeta functionpole question?
  • · Replies 2 ·
Replies
2
Views
3K
Trivial zeros in the Riemann Zeta function
  • · Replies 2 ·
Replies
2
Views
5K
A problem on linear transformation and standard basis
  • · Replies 7 ·
Replies
7
Views
5K
Is a number preceding infinity, finite?
  • · Replies 26 ·
Replies
26
Views
7K
Good Books on Optimization Theory
  • · Replies 2 ·
Replies
2
Views
3K
Showing that a map from factor group to another set bijective
  • · Replies 2 ·
Replies
2
Views
3K
Confusion regarding the basis of A and the basis of Range of A
  • · Replies 1 ·
Replies
1
Views
2K
Problem involving eigenvalues/vectors
  • · Replies 9 ·
Replies
9
Views
3K
Determining groups not sure how to prove it.
  • · Replies 4 ·
Replies
4
Views
4K
For which L(s) will be these vectors linearly dependent?
  • · Replies 3 ·
Replies
3
Views
2K
How to get the derivative of this convex quadratic
  • · Replies 3 ·
Replies
3
Views
2K
Simple Q about direct product representation of a group
  • · Replies 1 ·
Replies
1
Views
2K
Understanding the Complex Inner Product: Definition and Importance
  • · Replies 3 ·
Replies
3
Views
2K
Eigenvector for Complex Eigenvalue help
  • · Replies 5 ·
Replies
5
Views
3K
Projection onto the kernel of a matrix
  • · Replies 2 ·
Replies
2
Views
7K
Maximum of arithmetic operations needed
  • · Replies 1 ·
Replies
1
Views
2K
Linear Algebra: Solve B^(-1) with A, C, D
  • · Replies 2 ·
Replies
2
Views
4K
Can Two Planes Meet at a Point Instead of a Line?
  • · Replies 3 ·
Replies
3
Views
3K
Test if 2 transformations produce equivalent relations to a reference
  • · Replies 1 ·
Replies
1
Views
2K
Is 0.9 Recurring Truly Considered Equal to 1 in Mathematics?
  • · Replies 34 ·
2
Replies
34
Views
17K
Positive Set in an Ordered Integral Domain
  • · Replies 1 ·
Replies
1
Views
3K
Can You Help with These Abstract Algebra Proofs?
  • · Replies 7 ·
Replies
7
Views
6K
What Are the Clopen Subsets in a Metric Space?
  • · Replies 3 ·
Replies
3
Views
5K
Why Are Complex Numbers Essential for Finding Nth Roots of Numbers?
  • · Replies 7 ·
Replies
7
Views
4K
Does φ(N) Form a Normal Subgroup in G' When φ is a Homomorphism?
  • · Replies 2 ·
Replies
2
Views
2K
What can I use to solve a general matrix?
  • · Replies 3 ·
Replies
3
Views
3K