From the course: Machine Learning Foundations: Linear Algebra
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Changing basis of vectors
From the course: Machine Learning Foundations: Linear Algebra
Changing basis of vectors
- Numerous supplied machine learning problems can be reduced by changing from one coordinate system to another coordinate system, which is basically the same as changing from one basis to another. Up until now we have learned that the vector is an object that takes you from the origin into some point in space. A coordinate system is defined by unit vectors that we have named I and J. Now, we are going to define them as 'e one' and 'e two'. These unit factors have coordinates one zero and zero one respectively. Every vector in space is a unique combination of these basis vectors. Let's define vector 'a' that will be four units along 'e one' and three units down along 'e two'. So, vector 'a' is equal to vector sum four 'e one', plus minus three 'e two', or we can write it down as a list, four minus three. Basis vectors, form basis for space. And any vector in this space can simply be written as a linear combination of…
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