8464956
Description
Flashcards by William Hartemink, updated more than 1 year ago
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Created by William Hartemink
about 7 years ago
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| Question | Answer |
| Define: vector space | |
| Define: subspace | |
| Define: null space | |
| Define: column space | |
| Theorem: Is the column space of an m x n matrix a subspace of R^n or R^m? | |
| The column space of an m x n matrix is all of R^m iff... | |
| Define: linear transformation (think 2 properties) | |
| What makes an indexed set of vectors linearly independent? | |
| Define: basis | |
| The Spanning Set Theorem | |
| A basis for Col A is formed by which columns of matrix A? | |
| Define: The coordinates of a vector x relative to the basis Beta | |
| What kind of transformation is x -> [x]_B ? | |
| If a vector space V has a basis with n vectors, then any set in V containing more than n vectors must be _____________. | |
| If a vector space V has a basis of n vectors, then every basis of V must contain how many vectors? | |
| Define: Finite Dimensional and Infinite Dimensional vector spaces | |
| Let H be a subspace of V. What is the relationship between: dim H and dim V | |
| The Basis Theorem | |
| Define: Rank A | |
| The Rank Theorem: Rank A + dim Nul A = ? | |
| Invertible Matrix Theorem (continued) | |
| Change of Basis Theorem | |
| (Linear difference equations) If a_n != 0 and if {z_n} is given... | |
| The set of all solutions to the nth-order homogeneous linear difference equation is: |
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