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Finite-Dimensional Vector Spaces P.R. Halmos
Publisher: Springer

Even though I am not an undergraduate student (yet), I have to point out that this book is amazing as a first read for one good reason: Halmos forces the reader. In order to tackle the next topic in finite projective planes, we need a lightning introduction to finite-dimensional vector spaces. We have seen in the past the proof that every finite dimensional vector space is isomorphic to its double dual. Finite-Dimensional Vector Spaces book download Download Finite-Dimensional Vector Spaces The dimension of the vector space V over the field F can be written as dim F (V). For example, how does one explain the point of the abstract notion of finite-dimensional vector spaces when, unlike with groups, you don't seem to have an interesting collection of different spaces? You can always define an inner product and a norm if the vector space is finite-dimensional. Angles require something like an inner product. We did rank-nullity last time, and this time we're going to go over a few cool applications to rank-nullity. First, let's just say what everyone's thinking: there's just too many damn finite dimensional vector spaces to consider! Finite-Dimensional Vector Spaces: P.R.