Dependency tree

An arrow runs from a page to a page that rests on it: page B points at page A when some result on A depends, through the item graph, on a result whose home is B. Only pages in Linear Algebra are shown; anything this group rests on from elsewhere in the library is listed below.

Pages, prerequisites first

• Vector Spaces, Linear Subspaces, Span and Direct SumsExamples & counterexamples →
• Linear Independence, Bases and DimensionExamples & counterexamples →
• Linear Transformations, Rank-Nullity and Quotient SpacesExamples & counterexamples →
• Matrices, the Matrix of a Linear Map, and Change of BasisExamples & counterexamples →
• Gaussian Elimination, Elementary Matrices and Reduced Row Echelon FormExamples & counterexamples →
• Determinants of Matrices over a Commutative RingExamples & counterexamples →

Rests on other groups

• Bases and Dimension: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Suprema and Infima, The ZFC Axioms and the Basic Set Constructions
• Determinants of Matrices over a Commutative Ring rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Group Actions, Orbits, Stabilisers and Cayley's Theorem, Polynomial Rings, the Division Algorithm and Roots, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, Symmetric Groups, Cycle Decomposition and the Sign Homomorphism, The ZFC Axioms and the Basic Set Constructions
• Determinants over a Ring: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Group Actions, Orbits, Stabilisers and Cayley's Theorem, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, Symmetric Groups, Cycle Decomposition and the Sign Homomorphism, The ZFC Axioms and the Basic Set Constructions
• Gaussian Elimination and Row Reduction: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Gaussian Elimination, Elementary Matrices and Reduced Row Echelon Form rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Linear Independence, Bases and Dimension rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, The ZFC Axioms and the Basic Set Constructions
• Linear Transformations, Rank-Nullity and Quotient Spaces rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Linear Transformations, Rank-Nullity and Quotient Spaces: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Matrices and Change of Basis: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Matrices, the Matrix of a Linear Map, and Change of Basis rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Vector Spaces and Linear Subspaces: Examples and Counterexamples rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, The ZFC Axioms and the Basic Set Constructions
• Vector Spaces, Linear Subspaces, Span and Direct Sums rests on Binary Operations, Monoids, Groups and Subgroups, Construction of the Natural Numbers, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Rings, Subrings, Integral Domains and Fields, The ZFC Axioms and the Basic Set Constructions