From the course: Machine Learning Foundations: Linear Algebra

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Transforming to the new basis

Transforming to the new basis

From the course: Machine Learning Foundations: Linear Algebra

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Transforming to the new basis

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- [Instructor] We have explored matrix transformation in a simple example. Let's look at the fundamentals and rules behind it. Matrix transformations are a special class of functions that arise from matrix multiplication. In mathematics, we define an ordered n-tuple as a sequence of n real numbers and a solution of a linear system in n unknowns that can be written as x1 = s1, x2 = s2 until xn = sn. It can be expressed as an ordered n-tuple, s1, s2, until sn. We do know the set of all ordered n-tuples of real numbers with a bold capital letter R and superscript n. The elements for Rn are called vectors. Standard basis vectors are denoted as e1, e2, until en. All other vectors in Rn can be written in exactly one way is a linear combination of basis vectors. So if you have a vector x, it can be written as x = x1e1 + x2e2 + xnen. As matrix transformation is a special class of function, we usually use the letter T to…

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