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.
MHB How Can We Prove the Inequality of Rank Matrices?
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Graduate How do I supply arpack drivers with all starting vectors?
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Graduate Justify matrices form basis for SO(4)
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Undergrad Eistenstein series E_k(t=0) quick q? Modular forms
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MHB Jacobson Radical and Rad(M) - Bland Corollary 6.1.3 ....
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MHB Determining a determinant using recurrence relations
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Undergrad Congruence Subgroups and Modular Forms Concept Questions
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MHB How can we prove that E/Q is a normal extension?
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MHB Finitely Generated Modules and Maximal Submodules
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MHB Why is this polynomial separable?
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Graduate Representation number via quad forms of theta quadratic form
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Graduate Applying group theory to multivariate eqs
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MHB Showing that P_3 is a subspace to P_n
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MHB Eisenstein polynomial and field extension
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MHB Is t Algebraic Over F(S) in Field Extension E/F?
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Undergrad Can we retrieve the inverse of matrix A in this example?
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Graduate Matrix Lie groups and its Lie Algebra
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Undergrad Modular form quick question translation algebra
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Undergrad Geometric Algebra formulation of Quantum Mechanics
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MHB Why does this hold when we have the zero matrix?
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Undergrad Show that you can find d and b s.t pd-bq=1 , p and q are coprime- GCF
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Undergrad Automorphisms of Central Simple Algebras/Bresar Example 1.27
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MHB Determining Basis and Dimension for Vector Subspaces $U_1$ and $U_2$
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Insights Representations and Why Precision is Important
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MHB How to Extend These Vectors to a Basis in $\mathbb{R}^4$?
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MHB Determine the vectors of components
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Using Cayley-Hamilton Theorem to Calculate Matrix Powers
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MHB Solve Vector Space Question: Get the Solution Now
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MHB How to Quickly Find the Rank of a 4 x 6 Matrix Using Column Operations
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MHB Find the General Expression for a Linear Transformation
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Undergrad Multiplication Maps on Algebras .... Bresar, Lemma 1.25 ....
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Undergrad Calculating the Area of an Apollonian Gasket: A Formula for n Layers
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MHB Automorphisms of Central Simple Algebras - Bresar Example 1.27 .... ....
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MHB Left & Right Multiplication Maps on Algebras .... Bresar, Lemma 1.25 .... ....
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MHB No prefix added: How do I find a basis of a $\mathbb{R}$-vector space?
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Undergrad Multiplication Maps on Algebras .... Further questions ....
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MHB Are $V_1$ and $V_2$ Vector Spaces According to Defined Properties?
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Undergrad Prove the sequence is exact: 0 → ker(f) → V → im(f) → 0
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Undergrad Left/Right Multiplication Maps on Algebras .... Bresar
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MHB Simple Unitial Rings .... centre is a field .... ? ....
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MHB Characteristic Equations and Commutativity
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Undergrad Simple Unitial Rings .... centre is a field .... ? ....
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Undergrad Centre of an Algebra .... and Central Algebras ....
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MHB Centre of an Algebra .... and Central Algebras ....
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Graduate Modular forms, dimension and basis confusion, weight mod 1
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MHB How Do I Find the Eigenvalues of \(F^2\) for the Derivative Mapping in \(X\)?
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MHB Find Eigenvalues of 4x4 Matrix with -1 & 3 Entries
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MHB Comparing $gH$ and $Hg$ for Infinite & Finite Groups
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Undergrad First Weyl Algebras .... A_1 ....
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MHB First Weyl Algebras .... A_1 ....
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MHB Understanding Bresar's Example 1.10 on Simple Matrix Rings: Can Anyone Help?
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Undergrad Introduction to Simple Matrix Rings in Noncommutative Algebra
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Undergrad N-Dimensional Real Division Algebras
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MHB Subgroups of the dihedral group D6
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MHB Proving Determinant of Mirror-Image Identity Matrix
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MHB How can we compute the Galois group of a subgroup of a splitting field?
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Undergrad Frobenius Theorem - Bresar, Theorem 1.4 ....
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Undergrad Validity of proof of Cauchy-Schwarz inequality
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MHB Inverse of Giant $7 \times 7$ Matrix: Tips & Tricks
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MHB Permutation question concerning cycle shapes
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MHB Frobenius Theorem - Bresar, Theorem 1.4 ....
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MHB Finding 3 natural numbers by the rule of Sarrus
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Undergrad Bresar, Lemma 1.3 - Real Quaternions .... Division Algebras
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Undergrad Bresar, Lemma 1.2 - Finite Division Algebras ....
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Linear Algebra: characteristic polynomials and trace
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Undergrad Another Question about Finite Dimensional Division Algebras ....
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MHB Show that the set of the upper triangular matrices is a ring
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MHB Finite Dimensional Division Algebras - Bresar Lemma 1.1
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Undergrad Finite Dimensional Division Algebras - Bresar Lemma 1.1
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Undergrad First Sylow Theorem: Group of Order ##p^k## & Cyclic Groups
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MHB Determining when a system of equations has no solution and infinite solutions
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Undergrad A regular matrix <=> mA isomorphism
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Undergrad Unitary Matrix Representation for SU(2) Group: Derivation and Verification
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Graduate Understanding the Cost Function in Machine Learning: A Practical Guide
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High School Is identity matrix basis dependent?
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MHB The extension is Galois iff E is a splitting field of a separable polynomial of F[x]
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Undergrad What Does the Mysterious Symbol in a Formal Proof Represent?
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MHB Is This Matrix Idempotent?
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MHB How Do You Calculate Ore Production and Costs for Zinc and Aluminium?
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MHB Index of Positivity in Quadratic Form: $f(X) = \sum^{n}_{i=1} x_{2}^{i}$
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MHB Is there a more efficient way to determine the basis of a subspace?
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MHB Dimension of Dirac Functionals in $V$: Find the Answer
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MHB The extension is Galois iff H_i is a normal subgroup of H_{i-1}
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MHB Can the vectors be written as a linear combination?
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Undergrad From Non Hermitian to Hermitian Matrix
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MHB How Does Eisenstein's Criterion Confirm the Irreducibility of a Polynomial?
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Graduate (sum to infinity of divisor function)^{2} -- simplify the expression
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MHB Solve Exponential Fraction Equation for $α$ ($C$, $m$)
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Graduate Modular Forms: Non-holomorphic Eisenstein Series E2 identity
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MHB Show that the mapping is surjective
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MHB How to Prove Galois Extension Statements in a Normal and Separable Field?
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MHB How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?
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High School Understanding the Dagger Notation in Quantum Mechanics
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Undergrad Representing vectors with respect to a basis
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Undergrad Rotation Matrix for Vector v=(a,b,c) by Angle θ | Efficient Computation Method
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MHB Are Mutually Perpendicular Vectors Always Linearly Independent?
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Undergrad Why Is the Ratio of y2/y1 Not Constant for Linearly Independent Vectors?
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Undergrad Linear regression on data collection error
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Undergrad Orthogonal basis to find projection onto a subspace
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MHB Is Each Extension of Degree 2 Normal?
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