I often read that every tensor of order $2$ can be represented as a matrix (I do understand that). But not every matrix is the representation of some second order tensor. I am not sure, if I understand that correctly. Is it just that any matrix that represents a second order tensor has to be quadratic, i.e. a $n\times n$ matrix?
Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified:   Are matrices and second rank tensors the same thing? If the answer to 1 is yes, then can we think of a 3rd rank tensor as an ordered set of numbers in 3D lattice (just in the same way as we can think of a matrix as an ordered set of numbers in 2D lattice)?
When app is moved to SD card, where is the app data stored on SD card? I'm installing a brand new motion activated security light to an existing box on my garage. After removing the old light, I notice it only has white/black wiring while the new light fixture has of course white/black/green (ground) wires to attach. What do I do if no ground wire is available with the old box? Converting shapefile To GeoJSON using ArcPy? I know that a stationary metric is one which possesses a timelike Killing Vector (so I have time invariance).  I read that a static metric is one which has a timelike Killing vector (so it is stationary) AND this Killing vector is orthogonal to a family of hypersurface (of dimension n-1 is n is the dimension of my manifold). I don't understand the "physical" meaning behind this definition ? Is there a way to explain this in some more intuitive way ? Thanks In high school we learned to say "than I" and "as I" because you could potentially add an "am" to the end of the sentence.  Examples:  "She is smarter than I."  (Think: "...than I am.") "He is as tall as I."  (Think "...as I am.")  So analogously, shouldn't it be "like I" as well:  "He is sincere, just like I."  (Think: "... like I am.")  But universally, it seems that we use "like me".  Where does this reasoning break down?  Is there history here? What is a single word for a person who, as a habit, exaggerates a lot when relating information?   So for example, they relate something that happened but exaggerate so much that they are including clear falsehood and they are well known for doing that. Why won't QGIS recognize my GPS? Site-specific spellcheck? I often see misspelled words in titles and bodies of questions, only to see them spelled properly in the tags. I have to imagine that tags are always spelled right because it's hard to type arbitrary text into the tag box. I also have to imagine that sometimes autocorrect and spellcheck provided by browsers tend to turn programming terms and package names into English words. For example, see   Would it be possible to have some sort of spellchecker that compares text of titles (and maybe bodies) to known tags and offers some sort of correction (maybe red squiggles or something) when there's some statistical probability of a misspelling?  Since this would be using a site's tags, "magneto" would get corrected to "magento" on SO, while "magento" would get corrected to "magneto" on aviation.stackexchange.com.  In theory this could reduce a lot of stupid typos and prevent trivial edits just to fix the spelling of key words.  Note that this is not solving a problem that a user's browser can already solve because browsers ship with English dictionaries, not dictionaries of programming terms. In fact, it's potentially correcting a problem created by the browser (which might have already autocorrected "magento" to "magneto"). The locus of the intersection point of two perpendicular tangents to a given ellipse How to check iOS version? What oil is best for seasoning a cast-iron skillet Can any linear transformation be represented by a matrix? Use $\cal L$ to denote a linear transformation on some vector space. We know any matrix $\bf{A}$ can be viewed as a linear transformation by defining $\cal L:= \cal L(\bf{v})= Av$ where $\bf{v}$ is a vector. I am curious is any linear transformation can be represented by a matrix? If so, why? If not, can anyone help provide a counterexample?  In particular, projection of vectors onto a vector $\bf{b}$ is a linear transformation defined by ${\cal L(\bf{v})}=({\mathbf{v}} \cdot \frac{{\mathbf{b}}}{{|{\mathbf{b}}|}})\frac{{\mathbf{b}}}{{|{\mathbf{b}}|}}$. Can this linear transformation be represented by a matrix?  Thank you! doesn't has to /have to Integration by partial fractions; how and why does it work? Could someone take me through the steps of decomposing  $$\frac{2x^2+11x}{x^2+11x+30}$$ into partial fractions?   More generally, how does one use partial fractions to compute integrals $$\int\frac{P(x)}{Q(x)}\,dx$$ of rational functions ($P(x)$ and $Q(x)$ are polynomials) ?    This question is asked in an effort to cut down on duplicates. See .  Also see . How to use resistors? I have a power supply of 5 volts @ 1A. I want to reduce the current from 1A to 250mA. Which resistor should be use?   I tried this equation(Ohm's Law):  R = V / I  = 5/(0.75)  = 6.66 Ohms.  I tried the 6.66 Ohm resistor but it only reduce few mili Amps. I'd like to use a sequence of boxes to show how TeX works. I read some time ago that everything (or almost) in TeX are boxes.  So, how to show only the TeX boxes that surround each character, each line, each paragraph?  I'd like something similar to the image below, not fbox which contains blank space around it. What is inverse CDF Normal Distribution Formula Google Chrome PPA upgrade invalid signature How is prototyping done in a professional EE environment? Do you do your prototypes on breadboards, on copper clad boards, Manhattan style, or do you just draw schematics, order PCBs made and assembled and work with them, hacking here and there if necessary? Indicating a name change after publication My wife has publications under both her maiden name and her married name. How should she indicate that this is the case on her CV, if she wants to mention publications from both time periods?