User:Alexathkust/algebra

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first linear algebra

Contents

[edit] book a read

name arthor date other
Linear Algebra--An introduction to Abstract Mathematics Robert J. Valenza Sep 07- Dec 07 textbook of MATH217


[edit] common operator

Adjoint operator, Normal operator, Self-adjoint(Hermitian) operator, Unitary operator, Orthogonal operator


Name/Symbol Definition ⇔ ⇐ ⇒
Adjoint operator
T*		 Let T:V→W be a linear transformation, where V and W are finite-dimensional inner product spaces with inner products \langle \cdot,\cdot \rangle _1 and \langle \cdot,\cdot \rangle _2, respectively. A function T*:W→V is called an adjoint of T if \langle \rm{T}(x),y\rangle _2=\langle x,\rm{T}^*(y)\rangle _1 for all x\isin \rm{V} and y\isin \rm{W}. 　 　 　
Normal operator
TT*=T*T		 　 　 　 　
Self-adjoint(Hermitian) operator
T=T*		 　 　 　 　
Unitary operator
||T(x)||=||x|| (F=C)		 　 　 　 　
Orthogonal operator
||T(x)||=||x|| (F=R)		 　 　 　 　

[edit] list of proof

[edit] linear algebra

/definition /theorem /proposition