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