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The Matrix is everywhere. It is all around us. Even now, in this very room. You can see it when you look out your window or when you turn on your television. You can feel it when you go to work... when you go to church... when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.
But seriously- { { 2 5 7 }
{ 3 0 0 }
{ 2 9 2 } }
It is usually written with one pair of large brackets, like this:
/ 2 5 7 \
< 3 0 0 >
\ 2 9 2 /
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How do you find a negative matrix in algebra?
For example, if you have [ -4 1 0 3] as your matrix, it would be negative 4. Whatever negative number is in your matrix is your answer.
When is it important for a matrix to be square?
In the context of matrix algebra there are more operations that one can perform on a square matrix. For example you can talk about the inverse of a square matrix (or at least some square matrices) but not for non-square matrices.
Which type of matrix can be multiplied to another matrix and result in that matrix?
That is called the identity matrix. For example, (3,1,4)t x (1,1,1) = (3,1,4)t In this case (1,1,1) is the identity matrix. Another example is 5 11 1 0 1 11 x = 4 3 0 1 4 3 (You will have to imagine the brackets around the matrices as I did not know how to draw them in.) In this case 1 0 is the identity matrix. 0 1
How do you find rank of a matrix?
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
Can a Hermitian Matrix possess Complex Eigenvectors?
Yes. Simple example: a=(1 i) (-i 1) The eigenvalues of the Hermitean matrix a are 0 and 2 and the corresponding eigenvectors are (i -1) and (i 1). A Hermitean matrix always has real eigenvalues, but it can have complex eigenvectors.
