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? pic.twitter.com/vxIKeS4Lrq — Robert Low (@RobJLow) June 26, 2018

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Eigenvalues

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 colin@flyingcoloursmaths.co.uk 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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