
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: projection
Linear Algebra and Its Applications, Exercise 3.4.21
Exercise 3.4.21. Given the function on the interval , what is the closest function to ? What is the closest line to ? Answer: To find the closest function to the function we first project onto the function on the … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.10
Exercise 3.4.10. Given the two orthonormal vectors and and an arbitrary vector , what linear combination of and is the least distance from ? Show that the difference between and that combination (i.e., the error vector) is orthogonal to both … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.9
Exercise 3.4.9. Given the three orthonormal vectors , , and , what linear combination of and is the least distance from ? Answer: Any linear combination of and is in the plane formed by and . The combination closest to … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.8
Exercise 3.4.8. Project the vector onto the two nonorthogonal vectors and and show that the sum of the two projections does not equal (as it would if and were orthogonal). Answer: The projection of onto is . We have and … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.3
Exercise 3.4.3. Given the orthonormal vectors and and the vector from the previous exercise, project onto a third orthonormal vector . What is the sum of the three projections? Why? Why is the matrix equal to the identity matrix ? … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.2
Exercise 3.4.2. Given two orthonormal vectors and and the vector , project onto and . Also find the projection of onto the plane formed by and . Answer: Since is orthonormal, the projection of onto is given by Similarly the … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.1
Exercise 3.4.1. a) Given the following four data points: write down the four equations for fitting to the data. b) Find the line fit by least squares and calculate the error . c) Given the value of what is in … Continue reading