Engineering↗
Commutators, Homomorphisms, Kernels and Structure Maps
Handbook guide to measuring non-commutativity, structure-preserving maps, kernels, images and quotient-factorisation.
Tag
kernel
Every page in the KEVOS library tagged kernel. 11 pages.
Engineering↗
Group Isomorphism Theorems and Correspondence
Handbook guide to group isomorphism theorems and correspondence with core definitions, structural results, reasoning methods and verification checks.
Engineering↗
Ring Homomorphisms, Ideals and Kernel Methods
Handbook guide to ring homomorphisms, ideals and kernel methods, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Why Radical Functions Have Soluble Monodromy
Step-by-step structural proof that finite radical constructions have soluble monodromy, using direct products, quotients and commutative kernels.
Engineering↗
Gaussian Elimination over Finite Fields
Elimination over a finite field, structured methods for very large sparse systems, and why the linear algebra stage limits sieving methods.
Engineering↗
Kernel and Image of a General Matrix
Computing kernel and image bases for rectangular matrices over a field, and why the integer analogue is a different problem.
Engineering↗
LLL for Linearly Dependent Generating Sets
Extending LLL to generating sets that are not independent, and using the resulting zero vectors to extract relations.
Engineering↗
Radical Computation and the Ring of Multipliers
Computing the p-radical of an order as a kernel, and the ring of multipliers that enlarges the order.
Engineering↗
Regulator and Fundamental Unit Recovery
Extracting fundamental units and the regulator from the kernel of the relation matrix, and confirming the unit system is fundamental.
Engineering↗
The Berlekamp Factorisation Algorithm
Berlekamp's linear algebra approach to factoring over a finite field, the Berlekamp subalgebra, and when it outperforms the GCD pipeline.
Engineering↗
Abelian Categories
Additive and abelian categories, the axioms, exactness in a general abelian category, the Freyd-Mitchell embedding theorem, and the standard examples.
Related
Other tags in the library.
mathematics 387
abstract algebra 252
Machine Design 184
business 179
project management 158
Computational Number Theory 123
algebra handbook 85
graduate mathematics 85
handbook 79
templates and examples 78
History of Engineering 77
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algebra and trigonometry 74
universal algebra 62
algebra 60
project delivery 60
principles of project management 58
advanced algebra 53
Fasteners and Joints 53
Civil Engineering 48
CAD 42
Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
Power Transmission 34
template 34
Operational Excellence 32
example 31
project leadership 31
project teams 31
strategy 31
Business Expansion 29
Metrology 29
project management research 29
Sales & Marketing 29
personal development 27
behaviour change 26
habits 26
systems 26