Data Science in Theory and Practice. Maria Cristina Mariani

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A Subscript 3 comma 1 Baseline equals 7"/>.

      Definition 2.5 (Transpose of a matrix) The transpose operation

of a matrix changes the columns into rows, i.e. in matrix notation , where “” denotes transpose.

       Example 2.2

Definition 2.6 (Scaler multiplication of a matrix) The product of a scalar

, and a matrix is the matrix obtained by multiplying each entry in the matrix by the scalar:

      In other words,

.

      Definition 2.7 (Matrix addition) The sum of two vectors of the same size is the vector obtained by adding corresponding entries in the vectors:

      In other words,

.

      Definition 2.8 (Matrix multiplication) Suppose

is an

‐by‐

matrix and

is an

‐by‐

matrix. Then

is defined to be the

‐by‐

matrix whose entry in row

, column

, is given by the following equation:

      In other words, the entry in row

, column

, of

is computed by taking row

of

and column

of

, multiplying together corresponding entries, and then summing. The number of columns of

must be equal to the number of rows of

.

       Example 2.3

      then

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