conversations.from: human
conversations.value: a title for a book about C&eacute;sar, Madrid, Perez with the genre: Science & Math, Mathematics
conversations.from: assistant
conversations.value: A title for this book could be 'MATLAB Linear Algebra'
conversations.from: human
conversations.value: Give me the first five paragraphs for this book.
conversations.from: assistant
conversations.value: MATLAB Linear Algebra
  Command History | This presents a history of the functions introduced in the Command Window and allows you to copy and execute them (see the lower right part of Figure 1-2).
  Command Window | This is the window in which you execute MATLAB commands (see the central part of Figure 1-2).
  Workspace | This shows the present contents of the workspace and allows you to make changes to it (see the upper right part of Figure 1-2).
  Help | This allows you to search and read the documentation for the complete family of MATLAB products.
  Start button | This runs tools and gives you access to documentation for all MathWorks products currently installed on your computer (Figure 1-3).
conversations.from: human
conversations.value: Delete the last sentence.
conversations.from: assistant
conversations.value: MATLAB Linear Algebra
  Command History | This presents a history of the functions introduced in the Command Window and allows you to copy and execute them (see the lower right part of Figure 1-2).
  Command Window | This is the window in which you execute MATLAB commands (see the central part of Figure 1-2).
  Workspace | This shows the present contents of the workspace and allows you to make changes to it (see the upper right part of Figure 1-2).
  Help | This allows you to search and read the documentation for the complete family of MATLAB products.
conversations.from: human
conversations.value: Give me two more paragraphs.
conversations.from: assistant
conversations.value: The command close(h) deletes the figure identified by h. The command whitebg(h) complements all the colors of the figure h. The clf command closes the current figure. The command graymon sets defaults for graphics properties to produce more legible displays for grayscale monitors. The refresh command redraws the figure.
  Makes the existing axes e the current axes and brings the figure containing it into focus. The command gca returns the name of the current axes. The command cla deletes all objects related to the current axes.
conversations.from: human
conversations.value: Give me the last four paragraphs.
conversations.from: assistant
conversations.value: Consider the linear transformation f between two vector subspaces U (contained in R3) and V (contained in R4), such that for any point (a, b, c) in U:
  Hence the kernel is the set of vectors {0,b, 0} with varying b. Moreover, the kernel obviously has dimension 1, since it has {0,1,0} as a basis.
  The dimension of the image of f must match the rank of the matrix A, which we have just seen is 2. The columns of a two column submatrix of A which has a non-singular two by two submatrix will form a basis of the image of f.
  The rank of the quadratic form is 2, since the rank of the matrix is 2. The signature is also 2, since the number of positive terms in the diagonal matrix is 2.