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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 02/24/2012 for the course MECHANICAL 2.035 taught by Professor Rohanabeyaratne during the Spring '07 term at MIT.

Ask a homework question - tutors are online