# Imitrex imatrax

## C++ - CSR Matrix - Matrix multiplication - Stack

\begin [1, 0, 0] * \begin b_1 \\ \ine b_2 \\ \ine b_3 \end = b_1 [2, 1, 0] * \begin b_1 \\ \ine b_2 \\ \ine b_3 \end = 2b_1 b_2 [0, 0, 0] * \begin b_1 \\ \ine b_2 \\ \ine b_3 \end = b_3 \\ \begin 1 & 0 & 0 \\ \ine 2 & 1 & 0 \\ \ine 0 & 0 & 1 \end \begin b_1 \\ \ine b_2 \\ \ine b_3 \end = \begin b_1 \\ \ine 2 b_1 b_2 \\ \ine b_3 \end \end is ed an elementary row-addition matrix.

### Efficient sparse matrix-matrix products using colorings

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#### Inverse Matrix Calculator Inverse of a 3x3 Matrix

Matrices, when multiplied by its inverse will give a resultant identity matrix.

##### Linear Algebra - Matrix Matrix Multiplication

But to multiply a matrix by another matrix we need to do the "dot product" of rows and columns ... Let us see with an example: To work out the answer for the 1st row and 1st column: The "Dot Product" is where we multiply matching members, then sum up: (1, 2, 3) • (7, 9, 11) = 1×7 2×9 3×11 = 58 We match the 1st members (1 and 7), multiply them, likewise for the 2nd members (2 and 9) and the 3rd members (3 and 11), and finally sum them up. Here it is for the 1st row and 2nd column: (1, 2, 3) • (8, 10, 12) = 1×8 2×10 3×12 = 64 We can do the same thing for the 2nd row and 1st column: (4, 5, 6) • (7, 9, 11) = 4×7 5×9 6×11 = 139 And for the 2nd row and 2nd column: (4, 5, 6) • (8, 10, 12) = 4×8 5×10 6×12 = 154 And we get: DONE!

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