
Archives
 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
Tag Archives: orthogonal subspaces
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 3.1.20
Exercise 3.1.20. Suppose is a subspace of . Show that . What does this mean? Answer: We first consider the case where ; in other words, contains only the zero vector. From exercise 3.1.18 we know that . The only … Continue reading
Linear Algebra and Its Applications, Exercise 3.1.19
Exercise 3.1.19. State whether each of the following is true or false: (a) If the subspaces and are orthogonal, then and are also orthogonal. (b) If is orthogonal to and orthogonal to then is orthogonal to . Answer: (a) In … Continue reading
Linear Algebra and Its Applications, Exercise 3.1.9
Exercise 3.1.9. For the plane in spanned by the vectors and find the orthogonal complement (i.e., the line in perpendicular to the plane). Note that this can be done by solving the system where the two vectors are the rows … Continue reading
Linear Algebra and Its Applications, Exercise 3.1.8
Exercise 3.1.8. Suppose that and are orthogonal subspaces. Show that their intersection consists only of the zero vector. Answer: If and are orthogonal then we have for any vectors in and in . Suppose that is an element of both … Continue reading