norm - Norm of symbolic vector or matrix (2025)

Syntax Description Examples Magnitude of Symbolic Vector Compute 2-Norm of Matrix Effect of Assumptions on Norm Compute Different Types of Norms of Matrix Compute Different Types of Norms of Vector Input Arguments v — Input vector vector of symbolic scalar variables | symbolic matrix variable | symbolic function | symbolic matrix function p — Input 2 (default) | 1 | positive integer scalar | Inf | -Inf | "fro" A — Input matrix matrix of symbolic scalar variables | symbolic matrix variable | symbolic function | symbolic matrix function P — Input 2 (default) | 1 | Inf | "fro" X — Input array multidimensional array of symbolic scalar variables More About 1-Norm of a Matrix 2-Norm of a Matrix Infinity Norm of a Matrix Frobenius Norm of a Matrix and Multidimensional Array P-Norm of a Vector Frobenius Norm of a Vector Infinity and Negative Infinity Norm of a Vector Tips Version History R2022a: Compute Frobenius norm of symbolic array R2022a: Compute norm of symbolic matrix functions R2021a: Compute norm of symbolic matrix variables See Also MATLAB Command Americas Europe Asia Pacific References

syms x y zr = [x y z]

r =$$\left(\begin{array}{ccc}x& y& z\end{array}\right)$$

n = norm(r)

n =$$\sqrt{{\left|x\right|}^2+{\left|y\right|}^2+{\left|z\right|}^2}$$

A = inv(sym(magic(3)))

A =
$$\left(\begin{array}{ccc}\frac{53}{360}& -\frac{13}{90}& \frac{23}{360}\\ -\frac{11}{180}& \frac{1}{45}& \frac{19}{180}\\ -\frac{7}{360}& \frac{17}{90}& -\frac{37}{360}\end{array}\right)$$

norm2 = norm(A)

norm2 =
$$\frac{\sqrt{3}}{6}$$

norm2_vpa = vpa(norm2,20)

norm2_vpa =$$0.28867513459481288225$$

syms x yn = simplify(norm([x y]))

n =$$\sqrt{{\left|x\right|}^2+{\left|y\right|}^2}$$

assume([x y],"real")n = simplify(norm([x y]))

n =$$\sqrt{x^2+y^2}$$

assume(x,"clear")

A = inv(sym(magic(3)))

A =
$$\left(\begin{array}{ccc}\frac{53}{360}& -\frac{13}{90}& \frac{23}{360}\\ -\frac{11}{180}& \frac{1}{45}& \frac{19}{180}\\ -\frac{7}{360}& \frac{17}{90}& -\frac{37}{360}\end{array}\right)$$

norm1 = norm(A,1)

norm1 =
$$\frac{16}{45}$$

normf = norm(A,"fro")

normf =
$$\frac{\sqrt{391}}{60}$$

normi = norm(A,Inf)

normi =
$$\frac{16}{45}$$

norm1_vpa = vpa(norm1,20)

norm1_vpa =$$0.35555555555555555556$$

normf_vpa = vpa(normf,20)

normf_vpa =$$0.32956199888808647519$$

normi_vpa = vpa(normi,20)

normi_vpa =$$0.35555555555555555556$$

syms Vx Vy VzV = [Vx; Vy; Vz];norm1 = norm(V,1)

norm1 =$$\left|\mathrm{Vx}\right|+\left|\mathrm{Vy}\right|+\left|\mathrm{Vz}\right|$$

norm2 = norm(V)

norm2 =$$\sqrt{{\left|\mathrm{Vx}\right|}^2+{\left|\mathrm{Vy}\right|}^2+{\left|\mathrm{Vz}\right|}^2}$$

norm3 = norm(V,3)

norm3 =$${\left({\left|\mathrm{Vx}\right|}^3+{\left|\mathrm{Vy}\right|}^3+{\left|\mathrm{Vz}\right|}^3\right)}^{1/3}$$

normi = norm(V,Inf)

normi =$$\max \left(\left|\mathrm{Vx}\right|,\left|\mathrm{Vy}\right|,\left|\mathrm{Vz}\right|\right)$$

normni = norm(V,-Inf)

normni =$$\min \left(\left|\mathrm{Vx}\right|,\left|\mathrm{Vy}\right|,\left|\mathrm{Vz}\right|\right)$$

normf = norm(V,"fro")

normf =$$\sqrt{{\left|\mathrm{Vx}\right|}^2+{\left|\mathrm{Vy}\right|}^2+{\left|\mathrm{Vz}\right|}^2}$$