Browsing category matrices

A Matrix Definition of a Line

Every so often, I see a tweet so marvellous I can’t believe it’s true. Then I bookmark it and forget about it for months, until I don’t know what to write next. An example is @robjlow‘s message from June: Aren’t determinants wonderful? — Robert Low (@RobJLow) June 26, 2018

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I remember, with a faint feeling of dread, having to calculate the eigenvalues of a matrix. It became routine in the end, but I was recently reminded of the pain when a student asked if there was a shortcut. For a 2-by-2 matrix? Yes. It is up to you, though,

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Ask Uncle Colin: Invariant Lines

Dear Uncle Colin, I’ve got a matrix, and I’m not afraid to use it. It’s $\begin{pmatrix} 3 & -5 \\ -4 & 2\end{pmatrix}$ Apparently, it has invariant lines. Those, I’m afraid of. How do I find them? — Terrors About Rank, Safely Knowing Inverses Hi, TARSKI! An invariant line of

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How to invert a $3 \times 3$ matrix

So much wasted time. I spent much of my first two years at university cursing the names of Gauss and Jordan, railing at my lecturer (who grim-facedly assured me there were no more useful uses of a student’s thinking time than ham-fistedly rearranging these things), and thinking “there MUST be

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Ask Uncle Colin: a light matrix product

Dear Uncle Colin, I’m working on a (3D) computer graphics course, and my notes have some equations in that I don’t understand. I have a point light at (4D) position $\vec L$, an object translated by a 4D matrix $\bb M$ and a (4D) point on the surface at $\vec

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Matrix Determinants — TMTOWTDI

Oh, the days — weeks, even — of my university life I spent working out the determinants of matrices. The 3×3 version was the main culprit, of course, usually needing to be split down into three smaller determinants, and usually requiring a sign change in one or two that I’d

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Ask Uncle Colin: How do I look at matrices

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to and Uncle Colin will do what he can. Dear Uncle Colin How can you look at a matrix

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A reader asks… about matrices

A reader asks: I know that a square matrix $\mathbf{M}$ maps point $\mathbf{x}$ to point $\mathbf{y}$. Do I have enough information to work out $\mathbf{M}$? In a word: no, unless you’re working in one dimension! In general, to work out a square transformation matrix in $n$ dimensions, you need to

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