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.
Graduate Is absorption an axiom for a boolean algebra?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Determine the matrices that represent the following rotations of R^3
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Finding the elements of a group given two generators and relations
  • · Replies 26 ·
Replies
26
Views
8K
MHB A proof of a general property of norms
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Proof of a linear operator acting on an inverse of a group element
  • · Replies 4 ·
Replies
4
Views
3K
High School Help taking a cross product of a matrix
  • · Replies 3 ·
Replies
3
Views
3K
MHB Prove A=B when A⊂span(B) and B⊂span(A)
  • · Replies 2 ·
Replies
2
Views
2K
MHB Splitting Fields - Dummit and Foote - Example - page 541 - x^p - 2, p prime
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Understanding Mathematical Structures
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Linear independance best methods?
  • · Replies 11 ·
Replies
11
Views
10K
Graduate Can a 2N by 2N matrix written in terms of N by N matrices?
  • · Replies 3 ·
Replies
3
Views
4K
MHB Solving Equation System for Surjective Linear Transformation: T:R^4->R^2
  • · Replies 6 ·
Replies
6
Views
3K
MHB Redundancy in Question about Linear Transformations
  • · Replies 3 ·
Replies
3
Views
2K
MHB Matrix L1-Norm: Max of Column Sums Explained
  • · Replies 1 ·
Replies
1
Views
3K
MHB The Meaning of Degenerate in the Context of Linear Algebra
  • · Replies 2 ·
Replies
2
Views
3K
MHB Find a Basis for Subspace in P_3(\mathbb{R})
  • · Replies 11 ·
Replies
11
Views
3K
MHB Understanding Matrix Units for Linear Transformations in M2(Re)
  • · Replies 10 ·
Replies
10
Views
4K
Undergrad Would The Cross Product of x and x be z0?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Solving Linear Transformations w/ Bases of Vector Spaces
  • · Replies 4 ·
Replies
4
Views
3K
MHB Can $S_5$ be written as a multiple of $S_3$ and $S_2$?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Splitting Fields - Dummit and Foote - Exercise 1, page 545
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find the eigenvalue of a linear map
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Using linear algebra to find a number of independent equations
  • · Replies 5 ·
Replies
5
Views
4K
MHB Field Theory - Basic Theory - D&F Section 13.1
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Does a Linear Combination of Vectors in an Infinite Set Have to Be Finite?
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Solving Density Problems in Number Theory
  • · Replies 10 ·
Replies
10
Views
11K
MHB Determinant Property: Seen it Before? True?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 2, page 529
  • · Replies 4 ·
Replies
4
Views
2K
MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 4, page 530
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Some subset of a generating set is a basis
  • · Replies 11 ·
Replies
11
Views
6K
Undergrad Where Can I Find Linear Algebra Practice Problems for First Year Undergraduates?
  • · Replies 6 ·
Replies
6
Views
21K
MHB Solving $x$ in Terms of $a$: $x^4-3ax^3+3a^3x+a^4=0$
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Is Every Finite Dimensional Lie Algebra Isomorphic to a Subalgebra of GL(n)?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate If f and g are orthogonal, are f* and g orthogonal?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Cross product to find the area of a triangle
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Need help understanding Superposition Principle
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What is the cross product of 5k and 3i+4j?
  • · Replies 3 ·
Replies
3
Views
4K
MHB Can someone solve this System, (1equation, 3 variables)
  • · Replies 1 ·
Replies
1
Views
1K
MHB Algebraic Extensions: Dummit & Foote Section 13.2, Example 2 pg 526 - Help!
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Linearity of boolean expressions
  • · Replies 5 ·
Replies
5
Views
3K
MHB Field Theory - Algebrais Extensions - Dummit and Foote Section 13.2
  • · Replies 4 ·
Replies
4
Views
2K
Graduate If AB is invertible, then A and B are invertible.
  • · Replies 14 ·
Replies
14
Views
52K
Undergrad Squaring of vectors in absolute value
  • · Replies 5 ·
Replies
5
Views
4K
MHB Field Extensions - Dummit and Foote Chapter 13 - Exercise 2, page 519
  • · Replies 1 ·
Replies
1
Views
4K
MHB Confused About Exercise 11 Answer Key
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad What formula or principle governs this observed phenomena?
  • · Replies 2 ·
Replies
2
Views
3K
MHB Spanning set of vectors question
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proof of Eigenvector Existence for Linear Maps on Finite-Dimensional Spaces
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Can a point view another point around an obstructing point?
  • · Replies 4 ·
Replies
4
Views
3K
MHB Proof of a linear transformation not being onto
  • · Replies 6 ·
Replies
6
Views
2K
MHB Proving Linear Maps are One-to-One
  • · Replies 2 ·
Replies
2
Views
2K
MHB Field Theory - Dummit and Foote Ch 13 - Exercise 1, page 519
  • · Replies 11 ·
Replies
11
Views
4K
MHB Solving a system of linear equations with one unknown value
  • · Replies 1 ·
Replies
1
Views
12K
MHB 4x4 Matrix with rank B=4 and B^2=3
  • · Replies 7 ·
Replies
7
Views
3K
MHB Field Extensions, Polynomial Rings and Eisenstein's Criterion
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Do D&F Derive \(a(x)(1 + x) + b(x)(x^3 - 2) = 1\)?
  • · Replies 2 ·
Replies
2
Views
3K
MHB A linear transformation is invertible if and only if
  • · Replies 9 ·
Replies
9
Views
3K
MHB Finding the Unknowns: Solving a 4x4 Linear System of Equations
  • · Replies 6 ·
Replies
6
Views
2K
Graduate How Do Quaternions Enhance Understanding of 3D Rotations?
  • · Replies 14 ·
Replies
14
Views
6K
Graduate Algebraic properites of the direct sum
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad 2 Rotations on different coordinate systems
  • · Replies 7 ·
Replies
7
Views
4K
MHB Can You Find a Matrix with Ranking Requirements?
  • · Replies 8 ·
Replies
8
Views
3K
MHB What is the expression for |c_n| in terms of the given matrice?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Why Is the Dimension of the Solution Space n-r in Linear Algebra?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Linear transformation from [-1,1] to [a,b]
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solvable group: decomposable in prime order groups?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Problem involving matrix multiplication and dot product in one proof
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Equivalent statements to matrix A is orthogonal
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Should You Study All Proofs in Gallian's Abstract Algebra?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Eigenstate to eigenstate evolution with no intermediate superposition?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Linear Transformation: Does T(V) ⊆ W?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Non-linear multivariable functions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Looking for a proof regarding Baker-Campell-Hausdorff
  • · Replies 1 ·
Replies
1
Views
2K
MHB Algebraic Geometry Basics for Understanding Tensegrity in Masters Thesis
  • · Replies 7 ·
Replies
7
Views
3K
MHB Tensor notation for vector product proofs
  • · Replies 11 ·
Replies
11
Views
6K
Undergrad Is the Triple Scalar Product Always Zero?
  • · Replies 2 ·
Replies
2
Views
3K
MHB If c|ab and gcd(b, c) = 1 why does c|ac?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Roots and root vectors of sp(4,\mathbb{R})
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What Are the Benefits of Using Discrete Cosine Transform?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Closure in Groups: Definition & Examples
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What Does Zero Empirical Mean in Data Matrices?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How Does the Covariance Matrix Apply to Vectors X and Y?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Understanding Algebra: Step-by-Step Guide from vout to vcm and vd
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Proving the scalar matrices are the center of the matrix ring
  • · Replies 1 ·
Replies
1
Views
8K
Undergrad The sample covariance of N observations of K
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Extending the basis of a T-invariant subspace
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Question on conjugation closure of subgroups
  • · Replies 4 ·
Replies
4
Views
2K
MHB What are the properties of orthogonal matrices?
  • · Replies 15 ·
Replies
15
Views
4K
Graduate Direct sum of nullspace and range
  • · Replies 3 ·
Replies
3
Views
7K
MHB Tricky Linear Algebra Question. To show that an operator is 'cyclic'.
  • · Replies 6 ·
Replies
6
Views
3K
MHB Solving Householder Matrix Problem
  • · Replies 2 ·
Replies
2
Views
2K
MHB Construct Orthogonal Basis in R^3: Solve Exercise
  • · Replies 14 ·
Replies
14
Views
4K
Graduate Question about isomorphic mapping on direct sums?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Field Theory - Dummit and Foote - Chapter 13 - Theorem 6
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is the Direct Sum Complement Unique?
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Graph Plane x+2y+3z=0 | Math Tutorials
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Sample mean and sample covariance
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Generating a vector space via a T-cyclic subspace
  • · Replies 3 ·
Replies
3
Views
3K
MHB *3 coordinates of parallelogram STUV
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad What is the difference between Variance and Covariance?
  • · Replies 3 ·
Replies
3
Views
2K