Articles in matrix series

Positive Semi Definite

2019/2/7
| mathematic
PSD differential equation Any matrix $A_{d \times d}$ is said to be PSD if $x^TAx \geq$ 0 $\forall$ vector $x_{d \times 1}$. Examples Identity matrix $I_{d \times d}$: $$ A = \begin{bmatrix} 1 & 0 & 0 & 0 \newline 0 & 1 & 0 & 0 \newline 0 & 0 & 1 & 0 \newline 0 & 0 & 0 & 1 \end{bmatrix} $$ Then \begin{align} x^TAx &= \sum_{i = 1}^d \sum_{i = 1}^d A_{i,j}x_ix_j \newline &= \sum_{i = 1}^d A_{i,i} x_i^2\newline &= \sum_{i = 1}^d x_i^2 \newline &\geq 0 \end{align}……

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Matrix

2019/2/1
| mathematic
Determinant Calculation Determinant of 2x2 matrix $$ A= \begin{bmatrix} a & b \newline c & d \end{bmatrix} $$ $|A| = det(A) = ad -bc$ Determinant of 3x3 matrix, also called expansion of the determinant by first row. Link. $$ B= \begin{bmatrix} a & b & c \newline d & e & f \newline g & h & k \end{bmatrix} $$ $|B| = det(B) = a\begin{vmatrix} e & f \newline h & k \end{vmatrix} -b\begin{vmatrix} d & f \newline g & k \end{vmatrix} +c\begin{vmatrix} d & e \newline g & h \end{vmatrix}$……

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