Solve Invertible Matrix Problem: Find Equivalent Conditions to "A is Invertible

  • Thread starter Thread starter eyehategod
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary

Homework Help Overview

The discussion revolves around identifying all possible equivalent conditions for an nxn matrix A to be considered invertible. Participants are exploring various mathematical properties and definitions related to matrix invertibility.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to articulate different equivalent conditions for invertibility, such as the relationship between the determinant and invertibility, the existence of an inverse matrix, and properties related to row-echelon form. Some are questioning the clarity of the original problem and seeking further understanding.

Discussion Status

The discussion is active, with multiple participants contributing different perspectives on the conditions for invertibility. Some have provided specific conditions while others are still seeking clarification on the question itself. There is a variety of approaches being explored without a clear consensus yet.

Contextual Notes

Some participants express confusion regarding the question's requirements, indicating a potential lack of clarity in the problem statement. There may also be assumptions about prior knowledge of linear algebra concepts that are being questioned.

eyehategod
Messages
82
Reaction score
0
I have to write all possible equivalent conditions to "A is invertible," where A is an nxn matrix. can anyone help me out with this question
 
Physics news on Phys.org
Name one. You aren't trying very hard.
 
i don't understand the question
 
well you know that A^-1 = 1/det|A| *adj(A)

so for this to exist...det|A| can't be zero...and think of row-echelon form when finding A^-1

in row-echelon form, to get A^-1. how many non-zero rows must it have?How many pivot positions must it have?
 
Here's another one. A is invertible if there is a matrix B such that A*B=I. You are way behind. How about a statement in terms of the dimension of the kernel? How about expressing invertability in terms of the solutions to a system of linear equations? There's a lot of ways to express this concept.
 
A is also invertible when the determinant does not equal to 0
 

Similar threads

Matrix concept Questions (invertibility, det, linear dependence, span)
  • · Replies 4 ·
Replies
4
Views
2K
Prove there does not exist invertible matrix C satisfying A = CB
  • · Replies 6 ·
Replies
6
Views
2K
Not sure about this statement in vector space and matrix
  • · Replies 1 ·
Replies
1
Views
1K
If A^2 = 0, then A is not an invertible matrix
  • · Replies 4 ·
Replies
4
Views
5K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K
Matrix A is invertible iff A is onto?
  • · Replies 2 ·
Replies
2
Views
2K
Can a Matrix with Zero Eigenvalue Be Invertible?
  • · Replies 5 ·
Replies
5
Views
2K
Is Im(A) Equal to Im(AV) for an Invertible Matrix V?
  • · Replies 7 ·
Replies
7
Views
4K
Find a matrix ##C## such that ##C^{-1} A C## is a diagonal matrix
  • · Replies 9 ·
Replies
9
Views
2K
Linear Algebra Determinant proof
  • · Replies 4 ·
Replies
4
Views
1K