diff --git a/mat/cholesky.go b/mat/cholesky.go
index 3b0c2b02..68454d95 100644
--- a/mat/cholesky.go
+++ b/mat/cholesky.go
@@ -475,5 +475,5 @@ func (c *Cholesky) isZero() bool {
 }
 
 func (c *Cholesky) valid() bool {
-	return !c.isZero() && !c.chol.isZero()
+	return !c.isZero() && !c.chol.IsZero()
 }
diff --git a/mat/dense.go b/mat/dense.go
index d78c329c..5b7f6097 100644
--- a/mat/dense.go
+++ b/mat/dense.go
@@ -69,7 +69,7 @@ func (m *Dense) reuseAs(r, c int) {
 		// Panic as a string, not a mat.Error.
 		panic("mat: caps not correctly set")
 	}
-	if m.isZero() {
+	if m.IsZero() {
 		m.mat = blas64.General{
 			Rows:   r,
 			Cols:   c,
@@ -95,7 +95,7 @@ func (m *Dense) reuseAsZeroed(r, c int) {
 		// Panic as a string, not a mat.Error.
 		panic("mat: caps not correctly set")
 	}
-	if m.isZero() {
+	if m.IsZero() {
 		m.mat = blas64.General{
 			Rows:   r,
 			Cols:   c,
@@ -147,7 +147,9 @@ func (m *Dense) Reset() {
 	m.mat.Data = m.mat.Data[:0]
 }
 
-func (m *Dense) isZero() bool {
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. Dense matrices can be zeroed using Reset.
+func (m *Dense) IsZero() bool {
 	// It must be the case that m.Dims() returns
 	// zeros in this case. See comment in Reset().
 	return m.mat.Stride == 0
diff --git a/mat/dense_arithmetic.go b/mat/dense_arithmetic.go
index f3ab5c00..1f49d65f 100644
--- a/mat/dense_arithmetic.go
+++ b/mat/dense_arithmetic.go
@@ -467,7 +467,7 @@ func (m *Dense) Exp(a Matrix) {
 	}
 
 	var w *Dense
-	if m.isZero() {
+	if m.IsZero() {
 		m.reuseAsZeroed(r, r)
 		w = m
 	} else {
@@ -696,7 +696,7 @@ func (m *Dense) Outer(alpha float64, x, y *Vector) {
 		// Panic as a string, not a mat.Error.
 		panic("mat: caps not correctly set")
 	}
-	if m.isZero() {
+	if m.IsZero() {
 		m.mat = blas64.General{
 			Rows:   r,
 			Cols:   c,
diff --git a/mat/doc.go b/mat/doc.go
index a27a41bc..5a5cd9c7 100644
--- a/mat/doc.go
+++ b/mat/doc.go
@@ -36,10 +36,23 @@
 //  zero.Copy(a)
 //
 // Receivers must be the correct size for the matrix operations, otherwise the
-// operation will panic. As a special case for convenience, a zero-sized matrix
+// operation will panic. As a special case for convenience, a zero-value matrix
 // will be modified to have the correct size, allocating data if necessary.
 //  var c mat.Dense // construct a new zero-sized matrix
-//  c.Mul(a, a)       // c is automatically adjusted to be 6×6
+//  c.Mul(a, a)     // c is automatically adjusted to be 6×6
+//
+// Zero-value of a matrix
+//
+// A zero-value matrix is either the Go language definition of a zero-value or
+// is a zero-sized matrix with zero-length stride. Matrix implementations may have
+// a Reset method to revert the receiver into a zero-valued matrix and an IsZero
+// method that returns whether the matrix is zero-valued.
+// So the following will all result in a zero-value matrix.
+//  - var a mat.Dense
+//  - a := NewDense(0, 0, make([]float64, 0, 100))
+//  - a.Reset()
+// A zero-value matrix can not be sliced even if it does have an adequately sized
+// backing data slice, but can be expanded using its Grow method if it exists.
 //
 // The Matrix Interfaces
 //
diff --git a/mat/io.go b/mat/io.go
index d1c4c853..bcf32bcb 100644
--- a/mat/io.go
+++ b/mat/io.go
@@ -109,7 +109,7 @@ func (m Dense) MarshalBinaryTo(w io.Writer) (int, error) {
 // UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
 // it should not be used on untrusted data.
 func (m *Dense) UnmarshalBinary(data []byte) error {
-	if !m.isZero() {
+	if !m.IsZero() {
 		panic("mat: unmarshal into non-zero matrix")
 	}
 
@@ -158,7 +158,7 @@ func (m *Dense) UnmarshalBinary(data []byte) error {
 // UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
 // it should not be used on untrusted data.
 func (m *Dense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
-	if !m.isZero() {
+	if !m.IsZero() {
 		panic("mat: unmarshal into non-zero matrix")
 	}
 
@@ -268,7 +268,7 @@ func (v Vector) MarshalBinaryTo(w io.Writer) (int, error) {
 // UnmarshalBinary does not limit the size of the unmarshaled vector, and so
 // it should not be used on untrusted data.
 func (v *Vector) UnmarshalBinary(data []byte) error {
-	if !v.isZero() {
+	if !v.IsZero() {
 		panic("mat: unmarshal into non-zero vector")
 	}
 
@@ -301,7 +301,7 @@ func (v *Vector) UnmarshalBinary(data []byte) error {
 // See MarshalBinary for the on-disk layout.
 // See UnmarshalBinary for the list of sanity checks performed on the input.
 func (v *Vector) UnmarshalBinaryFrom(r io.Reader) (int, error) {
-	if !v.isZero() {
+	if !v.IsZero() {
 		panic("mat: unmarshal into non-zero vector")
 	}
 
diff --git a/mat/product.go b/mat/product.go
index dde0bff1..5a0343b7 100644
--- a/mat/product.go
+++ b/mat/product.go
@@ -71,7 +71,7 @@ func newMultiplier(m *Dense, factors []Matrix) *multiplier {
 	// allocate data for m.
 	r, c := m.Dims()
 	fr, fc := factors[0].Dims() // newMultiplier is only called with len(factors) > 2.
-	if !m.isZero() {
+	if !m.IsZero() {
 		if fr != r {
 			panic(ErrShape)
 		}
diff --git a/mat/symmetric.go b/mat/symmetric.go
index ee99a520..bf1fd571 100644
--- a/mat/symmetric.go
+++ b/mat/symmetric.go
@@ -126,7 +126,9 @@ func (s *SymDense) Reset() {
 	s.mat.Data = s.mat.Data[:0]
 }
 
-func (s *SymDense) isZero() bool {
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. SymDense matrices can be zeroed using Reset.
+func (s *SymDense) IsZero() bool {
 	// It must be the case that m.Dims() returns
 	// zeros in this case. See comment in Reset().
 	return s.mat.N == 0
@@ -138,7 +140,7 @@ func (s *SymDense) reuseAs(n int) {
 	if s.mat.N > s.cap {
 		panic(badSymCap)
 	}
-	if s.isZero() {
+	if s.IsZero() {
 		s.mat = blas64.Symmetric{
 			N:      n,
 			Stride: n,
@@ -283,7 +285,7 @@ func (s *SymDense) SymRankK(a Symmetric, alpha float64, x Matrix) {
 func (s *SymDense) SymOuterK(alpha float64, x Matrix) {
 	n, _ := x.Dims()
 	switch {
-	case s.isZero():
+	case s.IsZero():
 		s.mat = blas64.Symmetric{
 			N:      n,
 			Stride: n,
diff --git a/mat/triangular.go b/mat/triangular.go
index c613040e..db5cdc1a 100644
--- a/mat/triangular.go
+++ b/mat/triangular.go
@@ -135,7 +135,7 @@ func (t *TriDense) Dims() (r, c int) {
 // Triangle returns the dimension of t and its orientation. The returned
 // orientation is only valid when n is not zero.
 func (t *TriDense) Triangle() (n int, kind TriKind) {
-	return t.mat.N, TriKind(!t.isZero()) && t.triKind()
+	return t.mat.N, TriKind(!t.IsZero()) && t.triKind()
 }
 
 func (t *TriDense) isUpper() bool {
@@ -200,7 +200,9 @@ func (t *TriDense) Reset() {
 	t.mat.Data = t.mat.Data[:0]
 }
 
-func (t *TriDense) isZero() bool {
+// IsZero returns whether the receiver is zero-sized. Zero-sized matrices can be the
+// receiver for size-restricted operations. TriDense matrices can be zeroed using Reset.
+func (t *TriDense) IsZero() bool {
 	// It must be the case that t.Dims() returns
 	// zeros in this case. See comment in Reset().
 	return t.mat.Stride == 0
@@ -227,7 +229,7 @@ func (t *TriDense) reuseAs(n int, kind TriKind) {
 	if t.mat.N > t.cap {
 		panic(badTriCap)
 	}
-	if t.isZero() {
+	if t.IsZero() {
 		t.mat = blas64.Triangular{
 			N:      n,
 			Stride: n,
diff --git a/mat/vector.go b/mat/vector.go
index d63071b9..c405738e 100644
--- a/mat/vector.go
+++ b/mat/vector.go
@@ -67,7 +67,7 @@ func (v *Vector) SliceVec(i, k int) *Vector {
 // Dims returns the number of rows and columns in the matrix. Columns is always 1
 // for a non-Reset vector.
 func (v *Vector) Dims() (r, c int) {
-	if v.isZero() {
+	if v.IsZero() {
 		return 0, 0
 	}
 	return v.n, 1
@@ -76,7 +76,7 @@ func (v *Vector) Dims() (r, c int) {
 // Caps returns the number of rows and columns in the backing matrix. Columns is always 1
 // for a non-Reset vector.
 func (v *Vector) Caps() (r, c int) {
-	if v.isZero() {
+	if v.IsZero() {
 		return 0, 0
 	}
 	return v.Cap(), 1
@@ -89,7 +89,7 @@ func (v *Vector) Len() int {
 
 // Cap returns the capacity of the vector.
 func (v *Vector) Cap() int {
-	if v.isZero() {
+	if v.IsZero() {
 		return 0
 	}
 	return (cap(v.mat.Data)-1)/v.mat.Inc + 1
@@ -426,7 +426,7 @@ func (v *Vector) MulVec(a Matrix, b *Vector) {
 // reuseAs resizes an empty vector to a r×1 vector,
 // or checks that a non-empty matrix is r×1.
 func (v *Vector) reuseAs(r int) {
-	if v.isZero() {
+	if v.IsZero() {
 		v.mat = blas64.Vector{
 			Inc:  1,
 			Data: use(v.mat.Data, r),
@@ -439,7 +439,9 @@ func (v *Vector) reuseAs(r int) {
 	}
 }
 
-func (v *Vector) isZero() bool {
+// IsZero returns whether the receiver is zero-sized. Zero-sized vectors can be the
+// receiver for size-restricted operations. Vectors can be zeroed using Reset.
+func (v *Vector) IsZero() bool {
 	// It must be the case that v.Dims() returns
 	// zeros in this case. See comment in Reset().
 	return v.mat.Inc == 0