Linear and Abstract Algebra Forum

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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.
Undergrad Why does A squared not equal A times A when k = Z2?
  • Karl Karlsson
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Undergrad How to approach a cross product question
  • gregi_2
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2
Undergrad Three equations of planes, dimension should be 1?
  • JonnyG
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10
Undergrad Show that ##\mathbb{C}## can be obtained as 2 × 2 matrices
  • Karl Karlsson
  • · Replies 14 ·
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14
Connecting linear algebra concepts to groups
  • lemonthree
  • · Replies 6 ·
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6
Resource for learning linear algebra
  • Emekadavid
  • · Replies 5 ·
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5
What Are the Elements of (Z4×Z12)/<2,1>?
  • angubk6
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1
Undergrad How can I rotate a vector in 3D to match another vector's rotation?
  • kairama15
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2
Undergrad Finite fields, irreducible polynomial and minimal polynomial theorem
  • Karl Karlsson
  • · Replies 6 ·
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6
Undergrad Showing a set is a basis for a vector space
  • penroseandpaper
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2
Undergrad Subgroup axioms for a symmetric group
  • penroseandpaper
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Undergrad Why should a Fourier transform not be a change of basis?
  • Saw
  • · Replies 43 ·
2
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43
Group Homomorphism: True or False?
  • lemonthree
  • · Replies 1 ·
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1
Undergrad Understanding the concepts of isometric basis and musical isomorphism
  • KungFu
  • · Replies 3 ·
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3
High School Simple question about the dual space
  • etotheipi
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17
Undergrad Scalar powers of a matrix exponential
  • Hiero
  • · Replies 6 ·
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6
Find Point D on Plane for 4 Unit Cube Pyramid
  • jaychay
  • · Replies 3 ·
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3
How Does the Composite Transformation H Affect a Triangle and Arrow?
  • lemonthree
  • · Replies 1 ·
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1
What is the distance of closest approach
  • Another1
  • · Replies 2 ·
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2
Graduate What Does the Book Say About the Eigenvalues of 3x3 Matrices?
  • LagrangeEuler
  • · Replies 5 ·
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5
Undergrad Simple Generalized Eigenvalue problem
  • Trying2Learn
  • · Replies 17 ·
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17
Undergrad The Complete Solution to the matrix equation Ax = b
  • rtareen
  • · Replies 3 ·
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3
412.00.1.12 are relatively prime for all n.
  • karush
  • · Replies 1 ·
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1
Undergrad General Form of Fourth Rank Isotropic Tensor: A Scientific Inquiry
  • LuccaP4
  • · Replies 1 ·
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Undergrad What is the proper matrix product?
  • SVN
  • · Replies 9 ·
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9
Undergrad Is there any matrix equivalent for the Clifford product?
  • SVN
  • · Replies 1 ·
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1
Introduction to linear algebra
  • abs1
  • · Replies 3 ·
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3
Undergrad Question about the Galois correspondence
  • thaiqi
  • · Replies 13 ·
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13
Calculating LCD and GCD of 2 Sets of Numbers
  • karush
  • · Replies 2 ·
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2
Undergrad Theory of "fields" in the sense of fields in physics?
  • Stephen Tashi
  • · Replies 18 ·
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18
Undergrad What do you know about the planar product of two vectors?
  • LCSphysicist
  • · Replies 2 ·
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2
Undergrad Finding All Automorphisms of Group
  • jstrunk
  • · Replies 2 ·
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2
High School System of linear equations: When are we guaranteed a unique solution?
  • kent davidge
  • · Replies 5 ·
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5
How to determine the bases B and C
  • mathmari
  • · Replies 8 ·
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8
High School Solutions to systems of equations
  • kent davidge
  • · Replies 4 ·
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4
What Is the Upper Bound of Groups of Order in Finite Group Theory?
  • pauloromero1983
  • · Replies 2 ·
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2
Small Matrix Norm & Spectral Radius: Examples & Solutions
  • sarrah1
  • · Replies 8 ·
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8
Show that the subspace U is ϕ^z-invariant
  • mathmari
  • · Replies 4 ·
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4
Proving or disproving this matrix V is invertible.
  • kaienfr
  • · Replies 1 ·
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1
How to Translate Univariate Newton's Approximation to Multidimensional Systems?
  • Purplepixie
  • · Replies 2 ·
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2
Eigenspace is a subspace of V - ψ is diagonalizable
  • mathmari
  • · Replies 39 ·
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Undergrad Irreducible representations of the Dn group
  • Robin04
  • · Replies 3 ·
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3
Undergrad Matrices Commuting with Matrix Exponential
  • Isaac0427
  • · Replies 30 ·
2
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30
High School Vector Notation: Italic Boldface Symbolization
  • Anonymous1
  • · Replies 3 ·
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3
Undergrad Dot product in Euclidean Space
  • Trying2Learn
  • · Replies 16 ·
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16
Relations between map and matrix
  • mathmari
  • · Replies 10 ·
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10
How Do Polynomial Functions Transform When Applied to Matrices?
  • mathmari
  • · Replies 8 ·
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8
High School Do column 'vectors' need a basis?
  • etotheipi
  • · Replies 42 ·
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42
Show that these elements are linearly independent
  • mathmari
  • · Replies 12 ·
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12
What is the spectrum of φ - Eigenspace in finite fields?
  • mathmari
  • · Replies 15 ·
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15
Show that φ(v)=λv for a vector v and a coefficient λ
  • mathmari
  • · Replies 1 ·
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1
Undergrad Invertible Matrix Proof: A-Transpose * M * A (n by m)
  • Trying2Learn
  • · Replies 11 ·
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11
Proving the Formula for Determinants by Induction
  • mathmari
  • · Replies 4 ·
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4
High School How Is the Gradient Covariant in Different Coordinate Systems?
  • plob
  • · Replies 7 ·
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7
Undergrad Need help with tensors and group theory
  • Haorong Wu
  • · Replies 6 ·
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6
Undergrad Determining the Equation of a Sine and Cosine Graph that speeds up
  • FGD
  • · Replies 9 ·
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9
Undergrad Proving Lorentz Transformation identities
  • JD_PM
  • · Replies 20 ·
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20
Prove that the statements are equivalent
  • mathmari
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2
Undergrad Understanding Lorentz Groups and some key subgroups
  • JD_PM
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3
Proving Z[x] and Q[x] is not isomorphic
  • cbarker1
  • · Replies 5 ·
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5
How to prove an ideal of a ring R which is defined as a coordinates
  • cbarker1
  • · Replies 1 ·
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1
Undergrad What criteria identifies a math operation as a "product"?
  • ibkev
  • · Replies 14 ·
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14
Undergrad Explanation of a Line of a proof in Axler Linear Algebra Done Right 3r
  • MidgetDwarf
  • · Replies 4 ·
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4
Number of multiplications and divisions for LU decomposition
  • mathmari
  • · Replies 22 ·
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22
Understanding One-Sided Ideals in Mathematics
  • cbarker1
  • · Replies 5 ·
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5
Statements with linearly independent vectors
  • mathmari
  • · Replies 10 ·
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10
High School What are matrix transformations?
  • Sreekar adithya
  • · Replies 3 ·
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3
Undergrad This linear system has a solution? (Gauss' elimination)
  • requied
  • · Replies 19 ·
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19
311.1.4.6 create a vector equation
  • karush
  • · Replies 4 ·
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4
Creating Linearly Dependent Square Matrix from Cam Mechanism Equation
  • Barbudania
  • · Replies 2 ·
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2
Undergrad Rotate Functions with Derivatives: A Quantum Mechanics Homework
  • Oliver321
  • · Replies 2 ·
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2
Complete augmented by row operations
  • karush
  • · Replies 1 ·
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1
What is the next step in Gauss-Jordan Elimination for this augmented matrix?
  • karush
  • · Replies 7 ·
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7
Such a decomposition exists iff A is positive definite
  • mathmari
  • · Replies 13 ·
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13
What is the Meaning of Operation gx in Group Theory?
  • mathmari
  • · Replies 19 ·
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19
Orthonormal basis - Set of all isometries
  • mathmari
  • · Replies 23 ·
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23
Undergrad Spherical Harmonics Expansion convergence
  • Coltrane8
  • · Replies 6 ·
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6
Group mono-, endo-, iso-, homomorphism
  • mathmari
  • · Replies 9 ·
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9
Orthogonal Complement of Polynomial Subspace?
  • Displayer1243
  • · Replies 2 ·
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2
Is the composition of the isometries a rotation?
  • mathmari
  • · Replies 7 ·
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7
Subsets of permutation group: Properties
  • mathmari
  • · Replies 18 ·
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18
Understanding Vectors: Properties and Applications
  • mathmari
  • · Replies 4 ·
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4
Undergrad Linear Subspace with Neutral Element in Brazilian Portuguese and Spanish
  • LCSphysicist
  • · Replies 22 ·
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22
Undergrad How to solve a small system of non-linear equations?
  • Hypatio
  • · Replies 19 ·
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19
Undergrad Building a coefficient matrix for a system of equations
  • Hypatio
  • · Replies 7 ·
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7
How do unit vectors and eigenvalues relate to matrix A?
  • mathmari
  • · Replies 11 ·
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11
Test for compatibility of equations - Determinant |A b|
  • mathmari
  • · Replies 4 ·
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4
Show that there are vectors to get a basis
  • mathmari
  • · Replies 9 ·
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9
Kernel of Linear Map: Show $\ker \phi$ Equation
  • mathmari
  • · Replies 5 ·
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5
Undergrad Proving Convexity of the Set X = {(x, y) E R^2; ax + by <= c} in R^2
  • bonildo
  • · Replies 5 ·
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5
Undergrad The Paradox of u=v | Solve the Mystery
  • Gjmdp
  • · Replies 4 ·
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4
Is $2 + 8\sqrt{-5}$ a Unit or Irreducible in $\mathbb{Z} + \mathbb{Z}\sqrt{-5}$?
  • abs1
  • · Replies 5 ·
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5
Undergrad Logarithmic terms in a system of equations
  • Dilon
  • · Replies 4 ·
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4
Undergrad Given two linear transformations L and K, show ##K = \lambda L## holds
  • JD_PM
  • · Replies 9 ·
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9
Undergrad Find the parameter values that make ##L## surjective
  • JD_PM
  • · Replies 10 ·
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10
Method of least square: initial position & velocity
  • mathmari
  • · Replies 9 ·
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9
Projection Matrix Calculation for Vectors a_k: P_6P_5P_4P_3P_2P_1a_0
  • mathmari
  • · Replies 4 ·
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4
System no/infinitely many solution(s)
  • mathmari
  • · Replies 15 ·
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15
Is A Identical if A is a Square Matrix with Full Rank?
  • evinda
  • · Replies 6 ·
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6
Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)
  • Alex224
  • · Replies 3 ·
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3