QR factorization of $$$\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}}\end{array}\right]$$$

Find the QR factorization of $$$\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}}\end{array}\right]$$$.

Orthonormalize the set of vectors formed by the columns of the given matrix: $$$\left\{\left[\begin{array}{c}\frac{i a g h m n r s e^{e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]\right\}$$$ (for steps, see Gram-Schmidt calculator).

The columns of the matrix $$$Q$$$ are the orthonormalized vectors: $$$Q = \left[\begin{array}{c}\frac{i a g h m n r s e^{e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]$$$.

Find the transpose of the matrix: $$$Q^{T} = \left[\begin{array}{c}\frac{i a g h m n r s e^{e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]$$$ (for steps, see matrix transpose calculator).

Finally, $$$R = \left[\begin{array}{c}\frac{i a g h m n r s e^{e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}}\end{array}\right] = \left[\begin{array}{c}- \frac{a^{2} g^{2} h^{2} m^{2} n^{2} r^{2} s^{2} t^{2} e^{2 e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]$$$ (for steps, see matrix multiplication calculator).

$$$Q = \left[\begin{array}{c}\frac{i a g h m n r s e^{e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]$$$A

$$$R = \left[\begin{array}{c}- \frac{a^{2} g^{2} h^{2} m^{2} n^{2} r^{2} s^{2} t^{2} e^{2 e i n o r s^{2}}}{\left|{a g h m n r s}\right|}\end{array}\right]$$$A