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2. List of mathematical proofs - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_proofs

   Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges

3. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   Concerning general linear maps, linear endomorphisms, and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other parts of mathematics.

4. Hilbert's basis theorem - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_basis_theorem

   Hilbert's proof is highly non-constructive: it proceeds by induction on the number of variables, and, at each induction step uses the non-constructive proof for one variable less. Introduced more than eighty years later, Gröbner bases allow a direct proof that is as constructive as possible: Gröbner bases produce an algorithm for testing ...

5. Cramer's rule - Wikipedia

   en.wikipedia.org/wiki/Cramer's_rule

   In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...

6. List of theorems - Wikipedia

   en.wikipedia.org/wiki/List_of_theorems

   Amitsur–Levitzki theorem (linear algebra) Binomial inverse theorem (linear algebra) Birkhoff–Von Neumann theorem (linear algebra) Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension theorem for vector spaces (vector spaces, linear algebra)

7. Steinitz exchange lemma - Wikipedia

   en.wikipedia.org/wiki/Steinitz_exchange_lemma

   The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz .

8. Resolvent set - Wikipedia

   en.wikipedia.org/wiki/Resolvent_set

   In linear algebra and operator theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved". The resolvent set plays an important role in the resolvent formalism.

9. List of lemmas - Wikipedia

   en.wikipedia.org/wiki/List_of_lemmas

   1.3 Linear algebra. 1.4 Group theory. ... or sometimes intermediate technical results factored out of proofs). ... you can help by adding missing items. (August 2008)