8.15 Column and Row Partition of Identity Matrix

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 8.11 Colon Notation

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Column and Row Partition of Identity Matrix

Let $\vec{b} \in R^{1 \times n}$ . Then $\vec{b}$ can be written as a 6.1 Linear Combination of Vectors

\begin{aligned} [\vec{b}]_{1 \times n} & = y_{1} [{\vec{a}}_{1}]_{1 \times n} + y_{2} [{\vec{a}}_{2}]_{1 \times n} + \dots + y_{m} \cdot [{\vec{a}}_{m}]_{1 \times n} \\ = y_{1} [\begin{array}{c} a_{11} & a_{12} & \dots & a_{1 n} \end{array}] + y_{2} [\begin{array}{c} a_{21} & a_{22} & \dots & a_{2 n} \end{array}] + \dots + y_{m} [\begin{array}{c} a_{m 1} & a_{m 2} & \dots & a_{m n} \end{array}] \\ = y_{1} [A (1, :)] + y_{2} [A (2, :)] + \dots + y_{m} [A (m, :)] \\ = [{\vec{y}}^{T}]_{1 \times m} \cdot [A]_{m \times n} \end{aligned}