MDolphins said:The question is, find a 4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A.
So far, I have tried matrixes all involving 1's and 0's and -1's. I have also tried to use examples of nilpotent matrixes. However, I have not found anything close.
MDolphins said:The question is, find a 4x4 matrix A where A^2 and A^3 do not equal A, but A^4 = A.
So far, I have tried matrixes all involving 1's and 0's and -1's. I have also tried to use examples of nilpotent matrixes. However, I have not found anything close.
MDolphins said:I could come up with a rotation matrix that was 180 degrees but not one that was 360 degrees
MDolphins said:You are right. You'd want 270 degrees right?
MDolphins said:Oh okay so would it be by 120 degree angles. A2 would be 120 a3 would be 240 A4 would be 360 or the initial A
MDolphins said:Okay so now I have the angles, how can I visualize where I want the numbers in the4 x 4 matrix
MDolphins said:222222222
Ray Vickson said:Is that truly your response, or is some kind of hardware/software glitch messing up your answer on my display?
jtbell said:It's apparently his way of deleting all his posts in the thread. Fortunately you guys quoted enough of what he wrote so the thread still sort of makes sense!
A 4x4 matrix is a rectangular array of numbers or variables arranged in 4 rows and 4 columns. It is often used in linear algebra and can represent transformations, systems of equations, and other mathematical operations.
To determine if A^2 and A^3 do not equal A, you can multiply A by itself (A^2) and then by A again (A^3). If the resulting matrices are not equal to A, then A^2 and A^3 do not equal A.
It is important that A^4 equals A because it indicates that A is a projection matrix. This means that when A is applied to a vector, the resulting vector is in the same direction as the original vector, but possibly with a different magnitude.
Yes, A can still be a square matrix even if A^2 and A^3 do not equal A. This is because the property of A^4 = A is specific to projection matrices, but not all square matrices have to be projection matrices.
A 4x4 matrix A can be used in various real-world applications, such as computer graphics, image processing, and data compression. It can also be used to represent linear transformations in physics and engineering problems.