Prove help. rank of inverse matrix

In summary, the conversation is about proving that a certain type of matrix has the same rank as its transpose. The person is asking for help understanding an existing proof and is encouraged to attempt the proof themselves before seeking further assistance.
  • #1
pcming
6
0
I can't find out how to prove this question. Can anyone help?

Let A be an n x m matrix of rank m, n>m. Prove that (A^t)A has the same rank m as A.

Where A^t = the transpose of A.

I seen someone else have asked the question before and had got the answer. However I can't understand it. Hope someone can give me a more detail suggestion. Thanks!
 
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  • #2
You need to show some work first. You say you've seen a proof already but are having trouble understanding it, well what is the proof and which part is giving you trouble. There is more than one way to do it.

It's a good idea to attempt the proof yourself first without looking at the answer.

Edit: I just noticed the other thread you're talking about which has the answer you don't understand, and which ironically was written by me along ways back :rofl: I responded to your question in that thread.
 
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1. What is the rank of an inverse matrix?

The rank of an inverse matrix is the number of linearly independent rows or columns in the matrix. It represents the dimension of the vector space spanned by the rows or columns of the matrix.

2. How do you find the rank of an inverse matrix?

The rank of an inverse matrix can be found by performing row reduction on the matrix and counting the number of non-zero rows or columns in the reduced matrix.

3. What does the rank of an inverse matrix indicate?

The rank of an inverse matrix indicates the maximum number of linearly independent equations that can be obtained from the matrix. It also determines whether the matrix has a unique solution or not.

4. Can the rank of an inverse matrix be greater than the original matrix?

No, the rank of an inverse matrix cannot be greater than the original matrix. The inverse matrix has the same rank as the original matrix.

5. How does the rank of an inverse matrix affect its invertibility?

The rank of an inverse matrix determines its invertibility. If the rank of the matrix is equal to its order, then it is invertible. If the rank is less than the order, then the matrix is not invertible.

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