When I first learned about vectors over the summer, the zero vector was basically described as "pick a point on the x-y plane. Move 0 units up and 0 units to the right. That is the zero vector... just a dot on the x-y plane". This is assuming of course that you're talking about a vector $\vec{v}\in\mathbb{R}^2$.

Oct 25, 2014 · If $0$ were allowed as an eigenvector, suddenly every $\lambda \in \mathbb R$ would be an eigenvalue for it, rendering PCA meaningless because under its interpretation of the covariance eigenvectors, there would now be a "principal component" (the zero vector) with undefined variance attached.

So the zero vector axiom is actually the only axiom that forces a vector (sub)space to be non-empty. Hence, a vector (sub)space containing a zero vector is equivalent (in the presence of the other axioms) to it containing any vector at all. Since the zero vector is usually the easiest to find anyway, it's convenient to use its existence as an ...

Oct 28, 2012 · As well as being dangerous for anything except trivial types, what you wrote is pointless: constructing the vector with size length already default-initialises all of the new elements. If it were needed to default-initialise all elements later, or to set them all to some other value, std::fill() should be used because it's actually C++ and type ...

Feb 18, 2019 · If the context is the set of linear operators from one vector space to another then $0$ is the operator whose value at every point of the domain is the $0$ vector in the codomain. So the meaning of the symbol "$0$" changes depending on the context. That's potentially confusing (which is why you are asking the question.)

Aug 31, 2016 · Question Suppose we want to find a basis for the vector space $\\{0\\}$. I know that the answer is that the only basis is the empty set. Is this answer a definition itself or it is a result of the

Aug 29, 2018 · std::vector<int> v(100); // 100 is the number of elements. // The elements are initialized with zero values. You can be explicit about the zero values by using: std::vector<int> v(100, 0); You can use the second form to initialize all the elements to something other than zero. std::vector<int> v(100, 5); // Creates object with 100 elements.

By one of the axioms of field addition, $$0\cdot v=(0+0)\cdot v.$$ Since scalar multiplication is distributive over addition, $$(0+0)\cdot v=0\cdot v+0\cdot v.$$ From the previous two equalities we conclude that $$0\cdot v=0\cdot v+0\cdot v.$$ Adding to both sides the inverse element for addition of $0\cdot v$, which we'll denote by $-0\cdot v ...

A vector can exist with a zero magnitude and a direction. Express the vector as a scalar times a unit length vector. The unit length vector indicates the direction and the scalar represents the length. Even if the length goes to zero we still have the direction. This becomes obvious if we use polar or spherical coordinates.

Mar 27, 2016 · $\begingroup$ You'll normally label a vector $(0,\ldots,0)$ because it is the zero vector. In actual applications, you're most often not interested in $\mathbb{R}^n$ itself, but just use it as a convenient representation for some other vector space. $\endgroup$ –