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2. Quotient space (linear algebra) - Wikipedia

   en.wikipedia.org/.../Quotient_space_(linear_algebra)

   Formally, the construction is as follows. [1] Let be a vector space over a field, and let be a subspace of .We define an equivalence relation on by stating that iff .That is, is related to if and only if one can be obtained from the other by adding an element of .

3. Matrix similarity - Wikipedia

   en.wikipedia.org/wiki/Matrix_similarity

   In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that =. Similar matrices represent the same linear map under two (possibly) different bases, with P being the change-of-basis matrix.

4. File:A First Course in Linear Algebra for print.pdf - Wikipedia

   en.wikipedia.org/wiki/File:A_First_Course_in...

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5. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   Linear algebra is the branch of mathematics concerning linear equations such as: ... every submodule of a free module is free, ... Friedberg, Stephen H.; Insel, ...

6. Spectral theorem - Wikipedia

   en.wikipedia.org/wiki/Spectral_theorem

   In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the ...

7. Square root of a matrix - Wikipedia

   en.wikipedia.org/wiki/Square_root_of_a_matrix

   In linear algebra and operator theory, given a bounded positive semidefinite operator (a non-negative operator) T on a complex Hilbert space, B is a square root of T if T = B* B, where B* denotes the Hermitian adjoint of B.

8. File:Jim Hefferon - Linear Algebra (4th Edition).pdf - Wikipedia

   en.wikipedia.org/wiki/File:Jim_Hefferon_-_Linear...

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9. Rank–nullity theorem - Wikipedia

   en.wikipedia.org/wiki/Rank–nullity_theorem

   The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M ; and the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f ) and the nullity of f (the dimension of the kernel of f ).