Math 220 Defs
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| One to One Mapping | a mapping T:Rn -> Rm is 1-1 if for each vector b belongs to Rm, there is at most one x in Rn such that T(x) = b
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| Onto Mapping | a mapping T:Rn -> Rm is onto if Range(T) = Rm
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| Linear Transformation | a function that maps one vector space to another
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| Subspace | any set H in Rn that has the following 3 properties:
1) 0 vector belongs to H
2) for any u,v belongs to H, u+v belongs to H
3) for any u belongs to H and c belongs to R, uc belongs to H
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| Column Space of a Matrix | the set of a linear combinations of columns of A
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| Null Space of a Matrix | the set of all solutions of Ax=0
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| Linear Independance | a set of vectors s={v1...vp} is linearly independent if x1v1+...+xpvp=0 only has the trivial solution
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| Basis of a Subspace | a linearly independent set that spans a subspace H
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| Dimension of a Subspace | the number of vectors in any basis of a nonzero subspace H
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| Invertible Matrix | Anxn is invertible if there is a Cnxn such that CA=In and AC=In
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| Eigen Value of a Matrix | a number lambda is an eigen value if there is a nontrivial solution of Ax=lambdax
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| Eigen Vector of a Matrix | a nonzero vector x such that Ax=lambdax for some real number lambda
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| Similar Matrices | Anxn is similar to Bnxn if for some Pnxn, P-1AP = B
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| Diagonalizable Matrix | a matrix A is diagonalizable if A is similar to a diagonal matrix D
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