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  • linear algebra - Why are nonsquare matrices not invertible . . .
    I have a theoretical question Why are non-square matrices not invertible? I am running into a lot of doubts like this in my introductory study of linear algebra
  • In (relatively) simple words: What is an inverse limit?
    The inverse limit is a way to combine all of these approximations into an object in a consistent manner If you imagine your maps as going right to left, you have a branching tree that is getting "thinner" as you move left, and the inverse limit is the combination of all branches occurring "at infinity" Added
  • Example of Left and Right Inverse Functions
    I don't understand the question Do you want an example where there is a left inverse but not a right inverse or vice versa? If there is a left inverse and there is a right inverse, they must be equal
  • differential geometry - How is the definition of a regular curve . . .
    The definition of a regular curve is usually given by the non-vanishing of the tangent vector to every parametrization of curve at every point on the interval On the other hand, the definition of a regular surface is given by saying that it is a subset of $\mathbb R^3$ with all the standard properties
  • Why is transpose not equal to inverse in general?
    When you choose a basis (and a dual basis) you are fixing isomorphisms to $\mathbb R^n$, but now you’re working with the same vector space If I choose $ (1,0), (0,1)$ as one basis, and $ (1,1), (1,-1)$ as another basis for $\mathbb R^2$ then define a matrix which takes a basis vector to a basis vector, then that sure does look like the identity map in these bases, but that’s really just
  • What is a multiplicative inverse? - Mathematics Stack Exchange
    The inverse of $x$ is not necessarily $1 x$; it depends on the space you are talking about The inverse of an element $a$ is defined to be the element $b$ such that $ab=1$, where $1$ is the multiplicative identity element





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