Matrix Invertability & Singularity: Explained

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A matrix cannot be both invertible and singular; if a matrix is invertible, it is classified as non-singular. A singular matrix has a zero determinant, making it impossible to obtain an inverse. In contrast, a non-singular matrix has a non-zero determinant, allowing for the calculation of its inverse. The concept of the pseudo-inverse is acknowledged as useful but is distinct from a true inverse. The discussion clarifies the definitions and relationships between these types of matrices.
phymatter
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if a matrix is invertable can it be singular ?
 
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The link says it calculates the pseudo-inverse. The pseudo-inverse is a well known and useful concept, but it is NOT the same as the inverse.

The answer to the OP's questiion is "no".
 
No, if a matrix is invertible it is said to be non-singular which is the exact opposite of singular.
In other words a singular matrix has got a zero determinant and as such it's inverse cannot be obtained.A non singular matrix has got the determinant not equal to zero and in the due course it's inverse can be obtained hence the name invertible matrix.
 
@AlephZero and kaliro - Point conceeded.

@phymatter please accept my apologies if my post was misleading.
 
thanks for everyone's help :)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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