Arrow __EXCLUSIVE__ Download Vector
Cristal Hoggle
quiver(X,Y,U,V) plots arrows with directional components U and V at the Cartesian coordinates specified by X and Y. For example, the first arrow originates from the point X(1) and Y(1), extends horizontally according to U(1), and extends vertically according to V(1). By default, the quiver function scales the arrow lengths so that they do not overlap.
When scale is a positive number, the quiver function automatically adjusts the lengths of arrows so they do not overlap, then stretches them by a factor of scale. For example, a scale of 2 doubles the length of arrows, and a scale of 0.5 halves the length of arrows.
quiver(___,LineSpec) sets the line style, marker, and color. Markers appear at the points specified by X and Y. If you specify a marker using LineSpec, then quiver does not display arrowheads. To specify a marker and display arrowheads, set the Marker property instead.
quiver(___,Name,Value) specifies quiver properties using one or more name-value pair arguments. For a list of properties, see Quiver Properties. Specify name-value pair arguments after all other input arguments. Name-value pair arguments apply to all of the arrows in the quiver plot.
Create a quiver plot of the subset you selected. The vectors X and Y represent the location of the base of each arrow, and U and V represent the directional components of each arrow. By default, the quiver function shortens the arrows so they do not overlap. Call axis equal to use equal data unit lengths along each axis. This makes the arrows point in the correct direction.
Display the gradient vectors as a quiver plot. Then, display contour lines in the same axes. Adjust the display so that the gradient vectors appear perpendicular to the contour lines by calling axis equal.
Line style, marker, and color, specified as a character vector or string containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics (line style, marker, and color).
Arrow scaling factor, specified as a positive number or 'off'. By default, the quiver function automatically scales the arrows so they do not overlap. The quiver function applies the scaling factor after it automatically scales the arrows.
Specifying scale is the same as setting the AutoScaleFactor property of the quiver object. For example, specifying scale as 2 doubles the length of the arrows. Specifying scale as 0.5 halves the length of the arrows.
To disable automatic scaling, specify scale as 'off' or 0. When you specify either of these values, the AutoScale property of the quiver object is set to 'off' and the length of the arrow is determined entirely by U and V.
Automatic scaling of arrow length, specified as 'on' or 'off', or as numeric or logical 1 (true) or 0 (false). A value of 'on' is equivalent to true, and 'off' is equivalent to false. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.
I ask this because in my linear algebra class, my professor never used arrow notation, so sometimes it wasn't obvious between distinguishing a scalar and a vector. (Granted, he did reserve $u$, $v$, and $w$ to mean vectors.) At the same time, my machine learning class used arrows to denote vectors, but I know some other machine learning literature chooses not to put arrows on top of their vectors.
Let us decide we mark an element $\mathbbR^3$ as a vector, so we write $\vecv$ for it.Now, we want to multiply it with a $3\times 3$ matrix, since it is a matrix there is no arrow, or is there? After all the $3\times 3$ matrices form a vector-space and sometimes we use that structure. So, $\vecA$?
For example when we show that for $P$ the characteristic polynomial we have $P(\vecA)= 0$. Wait, haven't we seen the polynomials as an example of an infinite dimensional vector space? Should be put an arrow there, too? Then we can have $\vecP(\vecA)\vecv$!
I tried to write this a bit playful. But the serious point is that one really switches the point of view somewhat frequently when doing mathematics, and the notion of 'vector' is not so clear cut, as plenty of structures are (also) vector space.
In somewhat advanced (pure) mathematics, it is thus not very common to use the notation with an arrow to mark elements as vector specifically. But, if in some context it seems useful, there is no problem with it either.
Usually, it's fine to not have an arrow over your vectors as long as you define that they are vectors. Although in any case, really, you should define it to be a vector with or without an arrow. Once you say "Let v be a vector" then no arrow is needed. If I remember correctly, one of my linear algebra professors didn't use arrows on theirs while my other professor who is an algebraist uses arrows. If you're using a lot of scalars and vectors, using arrows might be handy. Again, it's a matter of preference, convenience, and the "situation" you're in. If there were numerous scalars and vectors which I was dealing with, I would use arrows so it's easier to spot which is a vector and which is not.
Notation indicates some mathematical maturity but it doesn't say much. I think precision is a greater factor. A "mature" mathematician might put an arrow over v without defining it (though who are we kidding, I doubt such a mathematician exists -- it is mediocre practice). A more mature mathematician would define what they mean by v-arrow (or simply v) at the get-go. So define what you mean and you will be safe.
A $2\times2$ real matrix is a vector in the vector space of $2\times2$ matrices. The polynomial $t^2+t+3$ is a vector in the vector space of polynomials of degree at most three. The function $\sin(x)$ is a vector in the space of continuous functions. Should we put arrows on these?
I think the confusion lies in the term "vector". Most people think first of an element in $\mathbbR^n$ when they hear vector - maybe they were introduced to vectors like that in school, or they are just the most common they work with. And then the arrow above the symbol makes perfect sense.
But in mathematics, a vector is defined as an element in a vector space, and that can be pretty much any structure. $\mathbbR^n$ is just the most common example, but functions, matrices, every field (so in particular scalars), and many more are vectors as well.
I think it's a maturity issue in one sense, which is that when you're first introduced to vectors is likely to be the first time you're exposed to the fact that there are two different operations, both called multiplication and both written the same way. You need to learn that you can multiply scalar by scalar, or vector by scalar, but not vector by vector. And perferably understand why. Same issue for addition, you can add two scalars or two vectors, but not a vector to a scalar.
However, once you understand the difference and have become accustomed to distinguishing them in your mind, it's less useful to write them very differently, and might become an annoying overhead. Reserving letters still helps, and usually is enough to remember what everything is. So, putting arrows or underlines everywhere feels like too much. In typeset text you might continue to use bold for vectors because it doesn't make things look much more busy on the page, but in writing I think most people drop it.
Furthermore, like quid's answer says, you will eventually need to deal with more than one vector space at once, at which point having a notational convention that distinguishes "vectors in my vector space" from "everything else" is not sufficient anyway. So as you mature you have to rely on other means to understand what type of entity everything is.
Perhaps off-topic, but there's a related thing in computer programming called "Systems Hungarian notation", where every variable name contains a prefix denoting the data type of the variable. Almost everyone hates this, because in practice it's too much repetition of the same information. It's actually quite difficult to strike the "right" balance because it's a matter of taste. Using mathematical block capitals for special entities $\mathbbR$, latin vs. greek letters for vectors vs. scalars, $n$ for an integer, $q$ for a rational, $x$ for a real, $v$ for a vector, $a$ for a coeffient and $f$ for a function, uppercase for matrices, all seem perfectly sensible to most mathematicians although none is essential. Hanging decorations off your letters, though, starts to cross a line and so fewer people bother.
I will buck the consensus here and say that yes, all else being equal, putting arrows on vector quantities is a slight signal that either the author or the intended audience are beginning students or physicists.
In my experience, $\overset\rightharpoonupv$ and $\mathbfv$ are used more often in science and engineering (even at the research level). This explains why they are often used in lower division mathematics courses, since at this point most of the class is not a mathematics major. As you proceed through mathematics, you begin to see vector spaces like real numbers and function spaces, and it makes less sense to think of vectors as "different" from the other things you're working with. Once you start hearing the word "module" enough, the notation has almost completely disappeared. The only exceptions I have seen are in differential geometry and applied math. I don't think the notation is so much mathematically immature as it is associated with "spatial" thinking.
Pick one and stick to it (at least throughout each publication). Most of my aquaintances who are mathematicians just skip the arrows, as well as subscripts (i.e., $L^2$ in $\cdot_L^2$) with an explicit remark that it is obvious.
I'd suggest that in determining whether to use it or not, you should be thinking in terms of your readership's understanding of what you have written, not any personal impression they might draw. If the arrow notation will make things clearer to them use it.
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