Diagonalizable for Dummies
adjective
What does Diagonalizable really mean?
Hey there! So, "diagonalizable" is a math term that we use when we're talking about matrices. Now, a matrix is basically a bunch of numbers arranged in a grid, kind of like a big math puzzle. When we say a matrix is "diagonalizable," it means that we can rearrange the numbers in a certain way so that we end up with a special kind of matrix called a diagonal matrix.
Now, a diagonal matrix is like the cleanest, most organized version of a matrix you can think of. All the numbers are lined up in a nice, straight line along the main diagonal, like they're all standing in a row at attention. It's kind of like when you're organizing your toys or books and you line them up neatly on a shelf - that's what we're doing with the numbers in a diagonal matrix.
So, when we say a matrix is "diagonalizable," what we're really saying is that we can take all the numbers in the original matrix and rearrange them so that we end up with this neat and tidy diagonal matrix. It's like tidying up a messy room and putting everything in its proper place.
I hope that makes sense! Let me know if you have any more questions about it.
Now, a diagonal matrix is like the cleanest, most organized version of a matrix you can think of. All the numbers are lined up in a nice, straight line along the main diagonal, like they're all standing in a row at attention. It's kind of like when you're organizing your toys or books and you line them up neatly on a shelf - that's what we're doing with the numbers in a diagonal matrix.
So, when we say a matrix is "diagonalizable," what we're really saying is that we can take all the numbers in the original matrix and rearrange them so that we end up with this neat and tidy diagonal matrix. It's like tidying up a messy room and putting everything in its proper place.
I hope that makes sense! Let me know if you have any more questions about it.
Revised and Fact checked by Robert Williams on 2023-11-15 05:14:55
Diagonalizable In a sentece
Learn how to use Diagonalizable inside a sentece
- When a matrix can be broken down into a set of eigenvectors and eigenvalues, it is called diagonalizable.
- A symmetric matrix is always diagonalizable because it can be broken down into a set of orthogonal eigenvectors.
- The matrix [2 1 / 1 2] is diagonalizable because it has distinct eigenvalues and a full set of linearly independent eigenvectors.
- Not all matrices are diagonalizable, for example, a matrix with repeated eigenvalues and not enough linearly independent eigenvectors is not diagonalizable.
- An n x n matrix is diagonalizable if and only if it can be expressed as PDP^-1, where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix with the eigenvalues of A on the diagonal.
Diagonalizable Category
The domain category to which the original word belongs.
Diagonalizable Pertains To
Words to which the original word is relevant