Math
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Left inverse and right inverseMath/Linear algebra 2019. 10. 12. 10:08
1. Overview 2. Description 2.1 Tall matrix and left inverse Now the thing is that this matrix definitely does not have a full inverse. However, with a little bit of creativity, we can come up with a way to multiply this matrix to produce the identity matrix. However, what we are inverting is the product A transpose A. So it turns out that A transpose A inverse times A transpose A is going to pro..
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Diagonal and traceMath/Linear algebra 2019. 10. 10. 21:36
1. Description 1.1 Diagonal $$\boldsymbol{v}_{i}=A_{i,i},\: \: i=\left \{ 1,2,\cdots ,min(m,n) \right \}$$ 1.2 Trace The trace of an n × n square matrix A is defined as $$tr(\boldsymbol{A})=\sum_{i=1}^{m}A_{i,i}=\sum_{i=1}^{n}a_{ii}=a_{11}+a_{11}+\cdots +a_{nn}$$ where aii denotes the entry on the ith row as well as ith column of A. 2. Example 2.1 Diagonal $$diag\left ( \begin{pmatrix} 1 & -1 & ..
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Matrix and Matrix multiplicationMath/Linear algebra 2019. 10. 10. 16:54
1. Overview 2. Description 2.1 Notation $$\boldsymbol{A}=\begin{pmatrix} 1 & 6 & 0 \\ 7 & 2 & 4 \\ 4 & 1 & 1 \end{pmatrix}$$ $$a_{1,2}=6$$ 2.2 Block matrices $$\boldsymbol{A}=\begin{pmatrix} \boldsymbol{D} & \boldsymbol{0} \\ \boldsymbol{1} & \boldsymbol{D} \end{pmatrix}=\begin{pmatrix} 3 & 0 & 0 & 0\\ 0 & 4 & 0 & 0\\ 1 & 1 & 3 & 0\\ 1 & 1 & 0 & 4 \end{pmatrix}$$ $\boldsymbol{D}=\begin{pmatrix} ..