The Search Engine has been modified to pick up this lesson using the following keywords:
determinant
matrix
tranpose
inverse
adjoint
cofactor
The program is now ready to accept requests for the Determinant, Inverse, Transpose, or Adjoint of any size matrix. This will show you the entire math behind each of the 4 operations. One special feature added is the matrix display calculation and math work shown for each Co-Factor matrix step for the Adjoint calculation. Be advised that the adjoint calculation for 3x3 matrices or higher as well as the determinant is quite a lot of math to go through. I designed the adjoint to look just like this site here:
Mathwords: Adjoint
Warning messages have been programmed when attempting to determine the Determinant, Inverse, or Adjoint of a non-square matrix since they do not exist. The Transpose is set to handle any matrix dimension since that exists.
The search engine will be ready tonight on this, in approximately 2 hours. It is located on the Linear Algebra page. As always, please contact me for enhancements or errors.
Matrix: Determinant-Adjoint-Inverse-Transpose
Enjoy.
I've added 1 enhancement to this lesson. A practice matrix generator button will now generate a matrix for you if you run out of homework problems to do. See the instructions link at the top of the page for the generation matrix logic.
Essentially, a square matrix will be created for you as small as a 2 x 2 all the way up to a 5 x 5 with positive entries. From there, you would proceed the same as you would if you had entered a matrix manually. Press any of the 4 buttons to see that operation answer and math work.
Enjoy.
Enhancement update for this lesson:
Similar to the matrix operator lesson, the tables have been redesigned for better alignment and spacing.
There are now yellow color codes for each step in the determinant, adjoint, inverse, and traspose to better show which row/columns are being affected and which answer entry is being added.
The search engine and link remain the same for this lesson as well.
I humbly present a very large update to this lesson. This calculator is now able to determine the Eigen Equation (characteristic polynomial) of a square matrix as well as the trace.
For the eigen equation, I've setup the math (color coded) to look just like the determinant button calculation. This time, I've included jump links to an algebra lesson on my site if the interim determinant multiplication step includes algebra, and not just constants. I've tested this for a few matrices and the math looks like it works. Please advise of any errors or enhancements.
Perhaps down the line, I'll hyperlink any eigen equations to my quadratic/cubic/quartic solver if the end result matches one of those equations.
Have a great day.
I present the largest Linear Algebra Enhancement for 2010:
Gauss-Jordan Elimination! Using row echelon and reduced row echelon form, MC will get your matrix into a format to solve the system of equations
This is version 1, let me know if you have enhancements or suggestions.