Matrix cookbook - Part 2

20 January 2008 5:52 by Tomasz Korzeniowski

Today’s entry is continuation of my last post where I have introduced some basic information about matrices. In the next few lines I would like to share with you more definitions related to matrices and describe basic operations on it.

Let me start with definitions.

• Stochastic matrix is matrix whose sum of all row elements (or column elements) equal to 1.
• Triangularl matrix is matrix in which all elements above or below the principal have 0 value.
• Rank of matrix is equal to the number of linearly independent rows or columns it contains, whichever of these two numbers is smaller. It is worth to remember that rank of a square matrix is equal to the number of nonzero rows.
• Determinant is function that associates a scalar to a square matrix.
• Invertible matrix is matrix with a nonzero determinant.
• Regular matrix is a square matrix that determinant is not 0.
• Singular matrix is matrix that determinant is equal to 0.

Let me now show few basic operation on matrices. Let’s assume we have to matrices A and B.

• Addition
  
• Substraction
  
• Multiplication
  
• Calculation of matrix determinant
  

This entry was posted on Sunday, January 20th, 2008 at 5:52 pm and is filed under Machine learning. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

Leave a reply:

Name (required)

Mail (will not be published) (required)

Website

Submit