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The three most vexing computations in linear algebra are these
'''Linear algebra''' is the [[mathematical]] subject that studies [[vector]]s, vector spaces, linear maps, and systems of linear [[equation]]s. Branches of Linear algebra typically include Linear equations, Matrices, [[Matrix]] decompositions, Computations, Vectors, Vector spaces, Multilinear algebra, Affine space, Projective space.<ref>[http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=linear+algebra Merriam Webster definition of Linear Algebra]</ref>
'''Linear algebra''' is the [[mathematical]] subject that studies [[vector]]s, vector spaces, linear maps, and systems of linear [[equation]]s. Branches of Linear algebra typically include Linear equations, Matrices, [[Matrix]] decompositions, Computations, Vectors, Vector spaces, Multilinear algebra, Affine space, Projective space.<ref>[http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=linear+algebra Merriam Webster definition of Linear Algebra]</ref>
Linear algebra has numerous applications in [[engineering]], [[chemistry]] and [[physics]].
Linear algebra has numerous applications in [[engineering]], [[chemistry]] and [[physics]].
The three most vexing computations in linear algebra are these:
#linear equations
#least squares
#finding the eigenvalues of an ''n x n'' matrix for n > 3.
== Basic Concepts ==
== Basic Concepts ==
*[[Orthogonality]]
*[[Orthogonality]]
:*[[orthogonal matrix]]
:*projections
:*projections
:*Gram-Schmidt Process and QR Factorization
:*Gram-Schmidt Process and QR Factorization