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| What is a Linear Transformation? |
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Definition
| A mapping T between vector spaces V and W that preserves vector space addition and scalar multiplication |
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| How do you determine if a mapping is a linear transformation? |
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Definition
| Let V and W be vector spaces. The mapping T: V (arrow) W is a linear transform iff T(cu+v)=cT(u)+T(v) for every choice of u and v in V and c in R. |
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| What's The null space of a linear transformation? |
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Definition
| Null space is the set (more specific, subspace of Rn) of all vectors that get mapped to zero vector under transform T, denoted N(T) |
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| What's an orthonormal set? |
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Definition
| orthogonal set comprised solely of vectors w/norm[sqrt(summation elements^2)] = 1 |
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Definition
| a subset of a vector space that is closed under addition and scalar multiplication |
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| What are the eigenvalues of a diagonal matrix |
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Definition
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Definition
| column rank of a matrix A is the max # of linearly independent columns of A. |
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Definition
| Set of vectors in an inner product space is Orthogonal if vectors are mutually orthogonal |
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| whats an onto transformation? |
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Definition
| the range of T equals the codomain |
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| Whats Cauchy-Schwartz Inequality? |
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Definition
| If u and v are vectors in R^n then magnitude (u(dot)v) is less than or equal to norm(u)norm(v) |
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| What's the eigenvector, eigenvalue? |
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Definition
| If the action of a matrix on (nonzero) vector changes its magnitude but not its direction (or flips it) then vector is called eigenvector of matrix. |
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