midterm_1 - linear transformation on a vector space j an...

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2.035: Midterm Exam - Part 1 (In-class) Spring 2007 1.5 hours You may use the notes you took in class and any other handwritten notes in your own handwriting. No other sources should be used. ——————————————————————————————————————————— Problem 1: Explain each of the following concepts precisely (yet succinctly): a) a vector space; b) a set of linearly independent vectors; c) the dimension of a vector space; d) a basis for a vector space; e) the components of a vector in a basis; f) the scalar or inner product between two vectors; g) the distance between two vectors; h) an orthonormal basis; i) a linear
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Unformatted text preview: linear transformation on a vector space; j) an invariant subspace of a linear transformation; k) the null space of a linear transformation; ) a singular linear transformation; m) the components of a linear transformation in a basis; and n) the scalar invariants of a linear transformation. ——————————————————————————————————————————— Problem 2: Give an example illustrating each concept in Problem 1....
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