Perform arithmetic operations on symbols.

Syntax

A+B
A-B
A*B A.*B
A\B A.\B
A/B A./B
A^B A.^B
A' A.'

Description

+

Matrix addition. A + B adds A and B. A and B must have the same dimensions, unless one is scalar.

-

Subtraction. A - B subtracts B from A. A and B must have the same dimensions, unless one is scalar.

*

Matrix multiplication. A*B is the linear algebraic product of A and B. The number of columns of A must equal the number of rows of B, unless one is a scalar.

.*

Array multiplication. A.*B is the entry-by-entry product of A and B. A and B must have the same dimensions, unless one is scalar.

\

Matrix left division. X = A\B solves the symbolic linear equations A*X=B. Note that A\B is roughly equivalent to inv(A)*B. Warning messages are produced if X does not exist or is not unique. Rectangular matrices A are allowed, but the equations must be consistent; a least squares solution is not computed.

.\

Array left division. A.\B is the matrix with entries B(i,j)/A(i,j). A and B must have the same dimensions, unless one is scalar.

/

Matrix right division. X=B/A solves the symbolic linear equation X*A=B. Note that B/A is the same as (A.'\B.'). Warning messages are produced if X does not exist or is not unique. Rectangular matrices A are allowed, but the equations must be consistent; a least squares solution is not computed.

./

Array right division. A./B is the matrix with entries A(i,j)/B(i,j). A and B must have the same dimensions, unless one is scalar.

^

Matrix power. X^P raises the square matrix X to the integer power P. If X is a scalar and P is a square matrix, X^P raises X 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 entries A(i,j)^B(i,j). A and B must have the same dimensions, unless one is scalar.

'

Matrix Hermition transpose. If A is complex, A' is the complex conjugate transpose.

.'

Array transpose. A.' is the real transpose of A. A.' does not conjugate complex entries.

Examples

syms a b c d;
A = [a b; c d];
A*A/A
A*A-A^2

[ a, b]
[ c, d]

[ 0, 0]
[ 0, 0]

syms a11 a12 a21 a22 b1 b2;
A = [a11 a12; a21 a22];
B = [b1 b2];
X = B/A;
x1 = X(1)
x2 = X(2)

x1 =
(a21*b2-b1*a22)/(-a11*a22+a12*a21)

x2 =
(-a11*b2+a12*b1)/(-a11*a22+a12*a21)

See Also