noting that differentiation is linear
I guess this is because differentiation is an operation that has.. [ x + (x+ h) ] / (x+ h) where h approaches 0 So this operation is a linear operation. Not exponential.
15 Matching Annotations
- Oct 2022
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mml-book.github.io mml-book.github.io
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Differentiation Rules
in the courselink discussion. Sayana posted more rules for derivatives that can be helpful.
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by collecting these partial derivatives
gives a jacobian matrix here, defined right below
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The gradient is thenthe collection of these partial derivatives
the difference between the gradient and a partial derivative
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The generalization of the derivative to functions of sev-eral variables is the gradient
the difference between a derivative and a gradient
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- Sep 2022
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mml-book.github.io mml-book.github.io
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We typically write 〈x, y〉 instead of Ω(x, y)
noting the change in syntax/notation
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Figure 3.3 Fordifferent norms, thered lines indicatethe set of vectorswith norm 1. Left:Manhattan norm;Right: Euclideandistanc
Does anyone know what the axis are for this? x1, x2 and if more dimensions xi?
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Throughout this book, we will use the Euclidean norm (3.4) bydefault if not stated otherwise
noting the euclidean norm will be used as default for the rest of the book
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The Manhattan norm is also called `1 `1 normnorm.
I have had a few courses refer to the norms as L1, L2. they mention which norm it as at the bottom of the definition
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AA−1 = I = A−1A
I think this would of been useful to see in section 2.3. In it they use a B value.
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A′
Does A' have a name. seems linked random how they got this
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Definition 2.2 (Identity Matrix). In Rn×n, we define the identity matrix
Does anyone remember the functional use case of the identity matrix. it mentions multiplication below, however that appears to be just multiple by 1.
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From the first and third equation, it follows that x1 = 1
how did this get x1 = 1? I don't see from the 1st and 3rd equation this follows. I assume we add eq (1) and (3), however that does not create x1 = 1? there would still be an x2 left over
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- Oct 2021
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mml-book.github.io mml-book.github.io
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Example 4.1 (Testing for Matrix Invertibility)Let us begin with exploring if a square matrix A is invertible (see Sec-tion 2.2.2). For the smallest cases, we already know when a matrixis invertible. If A is a 1 × 1 matrix, i.e., it is a scalar number, thenA = a =⇒ A−1 = 1a. Thus a 1a = 1 holds, if and only if a 6= 0.For 2 ×2 matrices, by the definition of the inverse (Definition 2.3), weknow that AA−1 = I. Then, with (2.24), the inverse of A is
Directly relates to figure 1 and the paragraphs above
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Figure 4.1 A mindmap of the conceptsintroduced in thischapter, along withwhere they are usedin other parts of thebook.Determinant Invertibility CholeskyEigenvaluesEigenvectors Orthogonal matrix DiagonalizationSVD
As mentioned in the discussion board, I found this diagram very helpfully for understanding the chapter. hopefully it helps others.
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