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.

We were all deeply impressed with Graeme from the very beginning. [Lucas’] confidence radically changed within only 3 weeks of Graeme’s instruction and assistance. I am sure this was largely attributed to Graeme’s infectious passion and love for his subject, and his high personal level of skill, teaching experience and understanding of mathematics. Lucas always found Graeme could explain concepts so knowledgeably and easily, which really did transform Lucas’ appreciation and enjoyment of the subject. Graeme always gave Lucas assistance and time over and above his hour’s tutoring session. Graeme has developed a wonderful relationship and more of a mentoring role which has been of great assistance and value to Lucas as he faces the pressures of his final year of school. I have no hesitation in recommending Graeme as an outstanding tutor and friend, and a very wise, knowledgeable and capable teacher of the highest calibre.

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