List questions from projection-matrices

Published on 11 Apr 2026 - 4:53

318

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How to show $\text{rank}(p)=\text{trace}(p)$ for every projector $p$ defined on $\mathbb{R}^n$?

Published on 13 Apr 2026 - 5:52

79

Views

What is the intuition behind this (concrete) system of equations? (It has to do with orthogonal projections onto non-orthogonal subspaces)

Published on 15 Apr 2026 - 3:45

131

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Change of basis, where the new basis is unknown

Published on 15 Apr 2026 - 6:27

69

Views

How to show $x \in R(P)$ when if $P$ is orthogonal projector?

Published on 12 Apr 2026 - 9:48

64

Views

How to show $P_MP_N=0$ if $M \perp N$?

Published on 13 Apr 2026 - 18:56

42

Views

Show $A^TP_{R(A)}=A^T$ for all $A$ in $\mathbb{R}^{m \times n}$?

Published on 16 Apr 2026 - 4:07

48

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Projection and the Orthogonal Projection

Published on 10 Apr 2026 - 22:35

301

Views

Show that $(I − P)^2 = I − P$ if $P=P^2$

Published on 10 May 2026 - 21:55

46

Views

Projection and orthogonal vectors

Published on 14 Apr 2026 - 13:01

84

Views

Argument that the picture of P is in U

Published on 15 Apr 2026 - 13:04

130

Views

Projection on to subspace with positive constraint?

Published on 11 Apr 2026 - 22:18

298

Views

How to project a vector $x$ onto the eigen-space, i.e. $x = \sum_{i=1}^{n} \langle w_i, x \rangle v_i$?

Published on 14 Apr 2026 - 21:16

822

Views

Identity Matrix and Projection

Published on 10 Apr 2026 - 21:29

1.2k

Views

Why is the projection matrix $P = A(A^T A)^{-1} A^T$ left-multiplied by $A$?

Published on 16 Apr 2026 - 12:34

List Question

How do we derive the spectral projector associated with a simple eigenvalue?

How to show $\text{rank}(p)=\text{trace}(p)$ for every projector $p$ defined on $\mathbb{R}^n$?

What is the intuition behind this (concrete) system of equations? (It has to do with orthogonal projections onto non-orthogonal subspaces)

Change of basis, where the new basis is unknown

How to show $x \in R(P)$ when if $P$ is orthogonal projector?

How to show $P_MP_N=0$ if $M \perp N$?

Show $A^TP_{R(A)}=A^T$ for all $A$ in $\mathbb{R}^{m \times n}$?

Projection and the Orthogonal Projection

Show that $(I − P)^2 = I − P$ if $P=P^2$

Projection and orthogonal vectors

Argument that the picture of P is in U

Projection on to subspace with positive constraint?

How to project a vector $x$ onto the eigen-space, i.e. $x = \sum_{i=1}^{n} \langle w_i, x \rangle v_i$?

Identity Matrix and Projection

Why is the projection matrix $P = A(A^T A)^{-1} A^T$ left-multiplied by $A$?

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