Associated Matrix

Let $V$ and $W$ be vector spaces of dimension $n$ and $m$ respectively. Then let ${v_{1}, v_{2}, ... v_{n}}$ be basis of $V$ and let ${w_{1}, w_{2}, ... w_{n}}$ be basis of $W$ We then get.

$T (ν_{_{1}}) = a_{11} w_{_{1}} + a_{21} w_{_{2}} + ...... + a_{m 1} w_{_{m}} T (ν_{_{2}}) = a_{12} w_{_{1}} + a_{22} w_{_{2}} + ...... + a_{m 2} w_{_{m}} ⋮ ⋮ ⋮ ⋮ T (ν_{_{n}}) = a_{1 n} w_{_{1}} + a_{2 n} w_{_{2}} + ...... + a_{mn} w_{_{m}}$

Here the matrix A is called the matrix associated with T with respect to the bases $The matrix A = a_{11} ⋮ a_{m} \dots ⋱ \dots a_{n} ⋮ a_{m} {v_{1}, v_{2}, ......, v_{n}} and {w_{1}, w_{2}, .... w_{m}} .$

🪴 TJ's Notes 1.0

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Associated Matrix

Associated Matrix

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