Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2
The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several ...
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In the last video, along with the ideas of vector addition and scalar multiplication, I described vector coordinates, where's this back and forth between, for example, pairs of numbers and two-dimensional vectors. Now, I imagine that vector coordinates were already familiar to a lot of you, but there's another kind of interesting way to think about these coordinates, which is pretty central to linear algebra. When you have a pair of numbers that's meant to describe a vector, like [3, -2], I want you to think about each coordinate as a scalar, meaning, think about how each one stretches or squishes vectors, In the xy-coordinate system, there are two very special vectors: the one pointing to the right with length 1, commonly called "i-hat", or the unit vector in the...
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In the last video, along with the ideas of vector addition and scalar multiplication, I described vector coordinates, where's this back and forth between, for example, pairs of numbers and two-dimensional vectors. Now, I imagine that vector coordinates were already familiar to a lot of you, but there's another kind of interesting way to think about these coordinates, which is pretty central to linear algebra. When you have a pair of numbers that's meant to describe a vector, like [3, -2], I want you to think about each coordinate as a scalar, meaning, think about how each one stretches or squishes vectors, In the xy-coordinate system, there are two very special vectors: the one pointing to the right with length 1, commonly called "i-hat", or the unit vector in the...
