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I remember that in my freshman's year, my linear algebra teacher explained that every matrix (i.e., not only rotation matrices) has this property: each column i
by ziotom78 6y ago
I remember that in my freshman's year, my linear algebra teacher explained that every matrix (i.e., not only rotation matrices) has this property: each column is the result of the operation on each basis element in the old coordinate system. This is true even for rectangular matrices.
- rocqua 6y agoOnce you get this, you can start building matrices for any (finite dimensional) 'vector space' not just the standard 'vectors as a list of numbers'. All you need to do is to pick a basis for your vector space, and you can start to represent linear transformations as matrices w.r.t. that basis. Even cooler is when you let go of specific basis choices, and start talking about properties of linear transformations that do not depend on a choice of basis. Things like a determinant, eigenvalues, etc.