Sinossi
Excerpt from Lessons Introductory to the Modern Higher Algebra
The geometrical importance of this theory is now manifest. When we are given the equation of any curve or surface, the theory of linear transformations at once presents us with equations representing other curves and surfaces, and possessing permanent relations to the given one, which will be unaffected by any change of the axes of co-ordinates. And in like manner the same theory presents us with certain functions of the coefficients of the given equation, the vanishing of which must express a property of the given curve or surface, wholly independent of the choice of axes. Besides these geometrical applications, the theory has other important uses, which I shall not stop to enumerate.
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