MATLAB by rudra pratap

3.2 Matrix and Array Operations
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3.2 Matrix and Array Operations
3.2.1 Arithmetic operations
For people who are used to programming in a conventional language such as Pascal,
Fortran, or C, it is an absolute delight to be able to write a matrix product as C=A*B
where A is an m x n matrix and B is an n x k matrix. MATLAB allows
+
*
I
' (caret)
addition
subtraction
multiplication
division
exponentiation
to be carried out on matrices in straightforward ways as long as the operation makes
sense mathematically and the operands are compatible. Thus,
A+B or A-B
A*B
A/B
is valid if A and B are of the same size,
is valid if A's number of columns equals B's number of rows,
is valid and equals A · B- 1 for same-size square matrices, and
which equals A*A, makes sense only if A is square.
help arith
In all these commands, if B is replaced by a scalar, say a, the arithmetic operations
are still carried out. In this case, the command A+a adds a to each element
of A, the command Ma (or a*A) multiplies each element of A by a and so on.
Vectors are just treated as a single row or a column matrix and therefore a command
such as w=u*v, where u and v are same-size vectors, say m x 1, produces an
error (because you cannot multiply an m x 1 matrix with an m x 1 matrix), whereas
w=u*v' and w=u' *V execute correctly, producing the outer and inner products of the
two vectors, respectively (see examples in Fig 2.7 on page 41).
The left division: In addition to the normal or right division (/), there is a
left division (\) in MATLAB. This division is used to solve a matrix equation. In
particular, the command x=A \ b solves the matrix equation Ax = b. Thus A\ b is
almost the same as inv (A) *b but faster and more numerically stable than computing
inv (A) *b. In the deg