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edit approved Oct 3, 2016 at 12:44
Rodrigo de Azevedo
edit approved Oct 3, 2016 at 12:44
Rodrigo de Azevedo
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Transforming Nona non-invertible Matrixmatrix into Invertiblean invertible matrix

Given a non-invertible, diagonalizable matrix, $A$., I wish to transform it into another matrix $B$, which that satisfies:

  • $B$ is invertible
  • all non-zero eigenvalues of $A$, are also eigenvalues of $B$
  • all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors that correspond to the same eigenvalues of $B$

There'sThere are no other constraints on $B$.

What is the simplest way to calculate such a matrix $B$? (of course, there'rethere are infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

Transforming Non-invertible Matrix into Invertible

Given a non-invertible, diagonalizable matrix, $A$. I wish to transform it into another matrix $B$, which satisfies:

  • $B$ is invertible
  • all non-zero eigenvalues of $A$, are also eigenvalues of $B$
  • all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors that correspond to the same eigenvalues of $B$

There's no other constraints on $B$.

What is the simplest way to calculate such a matrix $B$? (of course, there're infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

Transforming a non-invertible matrix into an invertible matrix

Given a non-invertible, diagonalizable matrix $A$, I wish to transform it into another matrix $B$ that satisfies:

  • $B$ is invertible
  • all non-zero eigenvalues of $A$, are also eigenvalues of $B$
  • all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors that correspond to the same eigenvalues of $B$

There are no other constraints on $B$.

What is the simplest way to calculate such a matrix $B$? (of course, there are infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

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Dudi Frid
Dudi Frid
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Given a non-invertible, diagonalizable matrix, $A$. I wish to transform it into otheranother matrix $B$, which satisfies that all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors of $B$, and I have:

  • $B$ is invertible
  • all non-zero eigenvalues of $A$, are also eigenvalues of $B$
  • all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors that correspond to the same eigenvalues of $B$

There's no other constraints on $B$.

What is a simplethe simplest way to calculate such a matrix $B$? (of course, therre'rethere're infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

Given a non-invertible, diagonalizable matrix, $A$. I wish to transform it into other matrix $B$, which satisfies that all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors of $B$, and I have no other constraints on $B$.

What is a simple way to calculate such a matrix $B$? (of course, therre're infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

Given a non-invertible, diagonalizable matrix, $A$. I wish to transform it into another matrix $B$, which satisfies:

  • $B$ is invertible
  • all non-zero eigenvalues of $A$, are also eigenvalues of $B$
  • all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors that correspond to the same eigenvalues of $B$

There's no other constraints on $B$.

What is the simplest way to calculate such a matrix $B$? (of course, there're infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!

Source Link
Dudi Frid
Dudi Frid
  • 265
  • 1
  • 9

Transforming Non-invertible Matrix into Invertible

Given a non-invertible, diagonalizable matrix, $A$. I wish to transform it into other matrix $B$, which satisfies that all of the eigenvectors correspond to non-zero eigenvalues of $A$, are also eigenvectors of $B$, and I have no other constraints on $B$.

What is a simple way to calculate such a matrix $B$? (of course, therre're infinitely many such matrices, but I want an easy way to calculate some such a matrix $B$).

Thanks in advance!