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.

Our daughter Angelina was home schooled and from the start did not like maths. Over the years I have battled through, trying 5 different programs along the way. Angelina was surviving but not enjoying the journey but, when it came to algebra, the future looked dim. A friend recommended Graeme to me as her three sons had been tutored by him. She could not recommend him more highly. My daughter has just finished year 12 maths and did very well, thanks to Graeme (that would be an understatement). Graeme has a love for his subject and a genuine interest in his students. Graeme seems to meets his students where they are and tailors the lessons to meet their individual needs and interests. Graeme not only explains concepts clearly, but we all found him an interesting, knowledgeable and humble man. We are extremely happy that Graeme was recommended to us. Now our daughter is looking forward to uni with a grateful heart. We also could not recommend Graeme more highly.

Angela K (parent, 2013)

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