Arithmetic Operators + - * / \ ^ ' - Matrix and array arithmetic

+

Addition or unary plus. A+B adds A and B. A and B must have the same size, unless one is a scalar. A scalar can be added to a matrix of any size.

-

Subtraction or unary minus. A-B subtracts B from A. A and B must have the same size, unless one is a scalar. A scalar can be subtracted from a matrix of any size.

*

Matrix multiplication. C = A*B is the linear algebraic product of the matrices A and B. More precisely,

For nonscalar A and B, the number of columns of A must equal the number of rows of B. A scalar can multiply a matrix of any size.

.*

Array multiplication. A.*B is the element-by-element product of the arrays A and B. A and B must have the same size, unless one of them is a scalar.

/

Slash or matrix right division. B/A is roughly the same as B*inv(A). More precisely, B/A = (A'\B')'. See the reference page for mrdivide for more information.

./

Array right division. A./B is the matrix with elements A(i,j)/B(i,j). A and B must have the same size, unless one of them is a scalar.

\

Backslash or matrix left division. If A is a square matrix, A\B is roughly the same as inv(A)*B, except it is computed in a different way. If A is an n-by-n matrix and B is a column vector with n components, or a matrix with several such columns, then X = A\B is the solution to the equation AX = B. A warning message is displayed if A is badly scaled or nearly singular. See the reference page for mldivide for more information.

If A is an m-by-n matrix with m ~= n and B is a column vector with m components, or a matrix with several such columns, then X = A\B is the solution in the least squares sense to the under- or overdetermined system of equations AX = B. The effective rank, k, of A is determined from the QR decomposition with pivoting. A solution X is computed that has at most k nonzero components per column. If k < n, this is usually not the same solution as pinv(A)*B, which is the least squares solution with the smallest norm .

.\

Array left division. A.\B is the matrix with elements B(i,j)/A(i,j). A and B must have the same size, unless one of them is a scalar.

^

Matrix power. X^p is X to the power p, if p is a scalar. If p is an integer, the power is computed by repeated squaring. If the integer is negative, X is inverted first. For other values of p, the calculation involves eigenvalues and eigenvectors, such that if [V,D] = eig(X), then X^p = V*D.^p/V.

If x is a scalar and P is a matrix, x^P is x raised to the matrix power P using eigenvalues and eigenvectors. X^P, where X and P are both matrices, is an error.

.^

Array power. A.^B is the matrix with elements A(i,j) to the B(i,j) power. A and B must have the same size, unless one of them is a scalar.

'

Matrix transpose. A' is the linear algebraic transpose of A. For complex matrices, this is the complex conjugate transpose.

Array transpose. A.' is the array transpose of A. For complex matrices, this does not involve conjugation.

+A, -A

Yes

A+B, A+c, c+B

Yes

A-B, A-c, c-B

Yes

A.*B

Yes

A*c, c*B

Yes

A*B

No

A/c, c/B

Yes

A.\B, A./B

Yes

A\B, A/B

No

A.^B

Yes, if B has nonnegative integer values.

c^k

Yes, for a scalar c and a nonnegative scalar integer k, which have the same integer data type or one of which has type double

A.', A'

Yes

Binary addition

A+B

plus(A,B)

Unary plus

+A

uplus(A)

Binary subtraction

A-B

minus(A,B)

Unary minus

-A

uminus(A)

Matrix multiplication

A*B

mtimes(A,B)

Arraywise multiplication

A.*B

times(A,B)

Matrix right division

A/B

mrdivide(A,B)

Arraywise right division

A./B

rdivide(A,B)

Matrix left division

A\B

mldivide(A,B)

Arraywise left division

A.\B

ldivide(A,B)

Matrix power

A^B

mpower(A,B)

Arraywise power

A.^B

power(A,B)

Complex transpose

A'

ctranspose(A)

Matrix transpose

A.'

transpose(A)

x

1

2

3

y

4

5

6

x'

1 2 3

y'

4 5 6

x+y

5

7

9

x-y

-3

-3

-3

x + 2

3

4

5

x-2

-1

0

1

x * y

Error

x.*y

4

10

18

x'*y

32

x'.*y

Error

x*y'

4 5 6

8 10 12

12 15 18

x.*y'

Error

x*2

2

4

6

x.*2

2

4

6

x\y

16/7

x.\y

4

5/2

2

2\x

1/2

1

3/2

2./x

2

1

2/3

x/y

0 0 1/6

0 0 1/3

0 0 1/2

x./y

1/4

2/5

1/2

x/2

1/2

1

3/2

x./2

1/2

1

3/2

x^y

Error

x.^y

1

32

729

x^2

Error

x.^2

1

4

9

2^x

Error

2.^x

2

4

8

(x+i*y)'

1 - 4i 2 - 5i 3 - 6i

(x+i*y).'

1 + 4i 2 + 5i 3 + 6i