When the English mathematician James Joseph Sylvester (1814-1897) first used the term *matrix* in 1850, he probably had little idea what would develop from this simple concept!

Of course, the word had been in use for millenia, having been drawn directly from the Latin name for a pregnant animal (from *mater* = mother). By the later 14th century, it had come to mean uterus/womb. By the mid sixteenth century it had started to take on the meaing of a place where something develops. For James Joseph Sylvester, the *something* was a determinant. He viewed a ** matrix** as an array of numbers which could generate smaller square arrays of numbers (called

It was Sylvester’s friend Arthur Cayley (1821-1895) who first treated matrices as mathematical objects in their own right and began to develop an algebra of matrices in the late 1850s. Mathematicians raced to discover their properties. Could they be added and subtracted? What about multiplied and divided? Were any of the operations commutative or associative (i.e. did it matter what order you performed the operations)? Were some matrices equivalent to others? Were there identity matrices? The list of questions grew … as did mathematicians’ understanding of these amazing objects.

They are used to solve complex arrays of simultaneous equations, as operators to transform graphs and images in a vast number of ways (rotations, reflections, stretches, etc.), to simplify our understanding of vectors, tensors and geodesics in physics … and the list goes on! When you modify images using graphics software, or move through a landscape in a computer game, the operations that govern the video output are essentially matrix operations.

This is a rich and interesting field of study.

Please watch this space. I will add material as soon as I am able.

How I wish you could be my professor – I have been having a consistent problem with the chain rule for what seems like weeks. I couldn’t grasp it at all. The first couple minutes of your video – it all instantly clicked for me. You are a life saver and a wonderful teacher. Thank you so much for your explanations!!!!!!!

Taikrys (on a CCM YouTube video about the Chain Rule)

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