# Tag Info

7

It's traditional mathematical English to say "$x$ vanishes" to mean $x = 0$.

6

I don't think there is a common term in set theory for that. But in the context of linear algebra, it is frequent to say that two subspaces are independent when their intersection is the zero space.

5

Sets that have empty intersection are said to be disjoint. Subgroups of the same group, subspaces of the same vector space, and so on will never be disjoint, as they'll have at least one common element (the identity element of the group, the 0 vector, etc.) Sets with just one element are singletons, but it would be unusual to use that term about algebraic ...

5

Your interpretation is correct. "The Wronskian vanishes" means the Wronskian is equal to $0$.

3

If you look in a non-mathematical dictionary, you will often find both definitions. For example, http://www.oxforddictionaries.com/us/definition/american_english/quartile defines quartile as 1 Each of four equal groups into which a population can be divided according to the distribution of values of a particular variable. 1.1 Each of the three ...

2

The word quartile refers to both the four partitions (or quarters) of the data set, and to the three points that mark these divisions. After all, we can't have one without the other. When citing a value for a quartile, though, we are specifically referring to the three dividing points, else it'd be meaningless. Thus, the first, second, and third quartiles ...

2

In the context of subspaces of a vector space (or more generally, subgroups of a group), it is common to abuse terminology and call such subspaces disjoint. This abuse is generally harmless since it is obviously impossible for them to actually be literally disjoint. You could also call them (linearly) independent, though personally I think "disjoint" ...

2

"Unit" from "unity", from Latin unus meaning "one" (see uno, un, etc. in Romance languages). Thus, "1-like thing". In fact, even 1 itself is sometimes referred to as "unity", as in the term roots of unity.

1

(The question is basically answered in the comment) As a topological manifold is locally path connected, a connected manifold is automatically path connected, as a connected locally path connected topological space is path connected

1

I don't think $σ^2_{x,y}$ is good notation, since the covariances can be negative. Thinking of the "co-standard deviations" as being imaginary isn't very helpful either, because the covariance matrix is symmetric, so its eigenvalues are real. So in some sense everything that can be said about covariance "lives in the real numbers".

1

Note: This is really just a long comment - but maybe it's helpful. This seems to me to be purely a matter of context. I have never seen anything like this before, with only 3 quartiles - it's written into the word itself that there should be 4 (QUART-iles). That said, this kind of thing happens in mathematics relatively often - there will be multiple uses ...

1

The equation is a single thing. The plural of maximum is maxima. There are multiple places of maxima. So the proper sentence is: "$t=\frac{(2n+1)\pi}{2}$ represents the places of maxima". "represets" is singular, "places" and "maxima" plural. Better explanation of period of 5/2? The period isn't 5/2. There were 5/2 periods. I would say "the function ...

1

It is valid only if the operator norm is induced by the Euclidean norm. If you use $||\cdot||_1$ or $||\cdot||_{\infty}$, you'll get different expressions of the operator norm. In order to show that this equality holds when the norm on $\mathbb{R}^n$ is the Euclidean norm, you can diagonalize $A^TA$ in an orthonormal basis : there exists an orthogonal ...

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