diff --git a/mat64/matrix.go b/mat64/matrix.go
index 3f64388..a1f5d7b 100644
--- a/mat64/matrix.go
+++ b/mat64/matrix.go
@@ -695,6 +695,9 @@ func Norm(a Matrix, norm float64) float64 {
 		}
 		return lapack64.Lansy(n, rm, work)
 	case *Vector:
+		if rma.isZero() {
+			return 0
+		}
 		rv := rma.RawVector()
 		switch norm {
 		default:
diff --git a/mat64/matrix_test.go b/mat64/matrix_test.go
index ca340e6..56fef75 100644
--- a/mat64/matrix_test.go
+++ b/mat64/matrix_test.go
@@ -8,6 +8,9 @@ import (
 	"fmt"
 	"math"
 	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
 )
 
 var inf = math.Inf(1)
@@ -253,6 +256,22 @@ func TestNorm(t *testing.T) {
 	testOneInputFunc(t, "Norm_inf", f, denseComparison, sameAnswerFloatApprox, isAnyType, isAnySize)
 }
 
+func TestNormZero(t *testing.T) {
+	for _, a := range []Matrix{
+		&Dense{},
+		&SymDense{mat: blas64.Symmetric{Uplo: blas.Upper}},
+		&TriDense{mat: blas64.Triangular{Uplo: blas.Upper, Diag: blas.NonUnit}},
+		&Vector{},
+	} {
+		for _, norm := range []float64{1, 2, math.Inf(1)} {
+			panicked, message := panics(func() { Norm(a, norm) })
+			if panicked {
+				t.Errorf("unexpected panic for Norm(&%T{}, %v): %v", a, norm, message)
+			}
+		}
+	}
+}
+
 func TestSum(t *testing.T) {
 	f := func(a Matrix) interface{} {
 		return Sum(a)