Why are invertible matrices called 'non-singular'?
I don't know for sure the source of the term "singular", but one reason to call matrices singular when the determinant vanishes, is that curves and surfaces and manifolds have singularities, that is, non-smooth points, when the Jacobian matrix of …
Singular vs. Non-singular - Mathematics Stack Exchange
2020年2月17日 · I'm asking this for clarification. A matrix/system of equations is singular is there are infinite solutions, but iff there is a unique solution then its non-singular? I haven't learned how to take a
Why do we call this transformation non-singular?
I would guess because "nonsingular" makes it sound like the operator "comes with" another operator, namely its inverse (i.e., singular = all alone, no other friendly operators to hang out with). $\endgroup$ –
Is a nonsingular matrix not the same as an invertible matrix?
2018年3月30日 · And being nonsingular does not imply being invertible (unless the underlying ring is a field)? linear-algebra;
linear algebra - Prove that if $A$ is a positive definite matrix, then ...
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Strictly diagonally dominant matrices are non singular
2015年6月2日 · I try to find a good proof for invertibility of strictly diagonally dominant matrices (defined by $|m_{ii}|>;\sum_{j\ne i}|m_{ij}|$).
How can I tell if a matrix is singular or nonsingular?
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Diagonalizable vs full rank vs nonsingular (square matrix)
2016年6月4日 · A diagonalizable matrix does not imply full rank (or nonsingular). My problem is. Does full rank matrix (nonsingular) imply it is diagonalizable? Equivalently: Does a matrix with all its columns or rows linear independent imply all its eigenvectors are linear independently?
matrices - What's the relationship between singular, nontrivial and ...
This coefficient matrix can be nonsingular hence there are trivial solutions. So, $\vec p_1$, $\vec p_2$ and $\vec p_3$ are linearly independent . linear-algebra
Abstract Nonsingular Curves - Mathematics Stack Exchange
Sorry for resurrecting such an old post, but Section §1.6 of Hartshorne annoys me in the sense that the concept of "abstract nonsingular curve" is not used very much (if at all) in algebraic geometry.