QR decomposition
As far as I know, any matrix can be QR decomposed.
A ∈ R m × n A \in \mathbb{R}^{m \times n}A∈Rm × n , then AAcan beA is decomposed intoQ, RQ, RQ、R， A = Q R A=QR A=QR ,
there are two decomposition methods,
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Complete QR decomposition
where Q ∈ R m × m Q \in \mathbb{R}^{m \times m}Q∈Rm×m， R ∈ R m × n R \in \mathbb{R}^{m \times n} R∈Rm × n .
Among them, the multiplication of the part of the dashed box is all 0, which is meaningless, and we can simplify and omit it. -
Reduced QR decomposition
Q ∈ R m × k Q \in \mathbb{R}^{m \times k}Q∈Rm×k， R ∈ R k × n R \in \mathbb{R}^{k \times n} R∈Rk × n . wherek = min ( m , n ) k=min(m,n)k=min(m,n )
I understand that this is enough, and there are three solution methods, which will be supplemented later if necessary.