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Intro to orthogonal projection onto a subspace
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Intro to orthogonal projection onto a subspace
14:35
About this lesson
• Make \(y\) as the sum of two vectors \(\hat{y}\) and \(z\)
• Orthogonal basis \(\)→\(\) \(\hat{y}= \frac{y \cdot v_1}{v_1 \cdot v_1}v_1 + \cdots + \frac{y \cdot v_p}{v_p \cdot v_p}v_p\)
• Orthonormal basis \(\)→\(\) \(\hat{y}=(y\cdot v_1)v_1+\cdots +(y\cdots v_p)v_p\)
• \(z=y - \hat{y}\)
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Video 1 of 8
Intro to orthogonal projection onto a subspace
15 min
• Selected
Property: projection of y onto S equals y when y is in S
4 min
Best approximation theorem and finding the closest point in a subspace
12 min
Decomposing y into orthogonal components using projection onto span of V1
11 min
Verifying orthonormality and computing an orthogonal projection
12 min
Best approximation of y using orthogonal projection onto span of two vectors
10 min
Finding the closest point to y using orthogonal projection
9 min
Finding the closest distance from a vector to a subspace
11 min