-
Archives
- October 2021
- January 2021
- March 2019
- January 2018
- December 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- July 2016
- October 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- January 2011
- August 2010
- June 2010
- May 2010
- November 2009
-
Meta
Category Archives: linear algebra
Linear Algebra and Its Applications, Exercise 3.3.13
Exercise 3.3.13. Using least squares, find the line that is the best fit to the following measurements: at at at at Also, given the matrix find the projection of onto the column space . Answer: Assuming that the line in … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.12
Exercise 3.3.12. Given the subspace spanned by the two vectors and find the following: a) a set of basis vectors for b) the matrix that projects onto c) the vector in that has the minimum distance to the vector in Answer: … Continue reading
Posted in linear algebra
Tagged basis, column space, left nullspace, orthogonal complement, projection matrix
Leave a comment
Linear Algebra and Its Applications, Exercise 3.3.11
Exercise 3.3.11. Suppose that is a subspace with orthogonal complement , with a projection matrix onto and a projection matrix onto . What are and ? Also, show that is its own inverse. Answer: Given any vector we have where … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.10
Exercise 3.3.10. Given mutually orthogonal vectors , , and and the matrix with columns and , what are and ? What is the projection of onto the plane formed by and ? Answer: We have where the zero entries are the result … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.9
Exercise 3.3.9. Suppose that is a matrix such that . a) Show that is a projection matrix. b) If then what is the subspace onto which projects? Answer: a) To show that is a projection matrix we must show that and also … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.8
Exercise 3.3.8. Suppose that is a projection matrix from onto a subspace with dimension . What is the column space of ? What is its rank? Answer: Suppose that is a arbitrary vector in . From the definition of we know … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.7
Exercise 3.3.7. Given the two vectors and find the projection matrix that projects onto the subspace spanned by and . Answer: The subspace spanned by and is the column space where The projection matrix onto the subspace is then . We … Continue reading
Linear Algebra and Its Applications, Exercise 3.3.6
Exercise 3.3.6. Given the matrix and vector defined as follows find the projection of onto the column space of . Decompose the vector into the sum of two orthogonal vectors and where is in the column space. Which subspace is in? … Continue reading
Posted in linear algebra
Tagged column space, left nullspace, orthogonal subspaces, orthogonal vectors, projection matrix
6 Comments
Linear Algebra and Its Applications, Exercise 3.3.5
Exercise 3.3.5. Given the system with no solution, provide a graph of a straight line that minimizes and solve for the equation of the line. What is the result of projecting the vector onto the column space of ? Answer: … Continue reading
Posted in linear algebra
Tagged column space, error vector, least squares, projection
Leave a comment
Linear Algebra and Its Applications, Exercise 3.3.4
Exercise 3.3.4. Given expand the expression , compute its partial derivatives with respect to and , and set them to zero. Compare the resulting equations to to confirm that you obtain the same normal equations in both cases (i.e., using … Continue reading
My Math Homework 