класс с объединенным использованием удаленной функции в конструкторе

Я пытаюсь сделать класс матрицы 4 * 4, он построен из массива из 16 чисел с плавающей запятой, но я также хочу представить его как массив из 4 vec4 (для каждого столбца).
Проблема в том, что он не компилируется и выдает ошибку везде, где я вызываю конструктор mat4.
Мой mat4.h:

struct mat4 {

union
{
float elements[4 * 4]; // column major ordering, index = row + col * 4
vec4 columns[4];
};

mat4();
mat4(float diagonal);

mat4& mul(const mat4& other); //TODO: maybe return mat4
// vec4 getColumn(int colIndex);
static mat4 identity(); // construct and return an identity matrix
static mat4 orthographic(float left, float right, float bottom, float top, float near, float far); // boundaries (clipping planes)
static mat4 perspective(float fov, float aspectRatio, float near, float far);
static mat4 translation(const vec3& translation);
static mat4 scale(const vec3 &scale);
static mat4 rotation(float angle, const vec3 & axis);
friend mat4 operator*(mat4 left, const mat4 & right);
mat4& operator*=(const mat4 &other); //TODO: check that it fits with the vectors
friend std::ostream &operator<<(std::ostream &stream, const mat4 &m);
};

Мой mat4.cpp:

#include "mat4.h"mat4::mat4() {
for (int i = 0; i < 4 * 4; i++)
elements[i] = 0;
}
mat4::mat4(float diagonal) {
for (int i = 0; i < 4 * 4; ++i) {
elements[i] = 0;
}
for(int i = 0; i < 4; i += 1)
elements[i + i * 4] = diagonal;
}
mat4& mat4::mul(const mat4 &other) {
for (int i = 0; i < 4; ++i)        // col
for (int j = 0; j < 4; ++j) {  // row
float sum = 0;
for (int k = 0; k < 4; ++k)
sum += elements[j + k * 4] * other.elements[k + i * 4];
elements[j + i * 4] = sum;
}
return *this;
}

/*vec4 mat4::getColumn(int colIndex) {
//colIndex *= 4; // TODO: profile and see if it's the same as (colIndex * 4) in each cell
return vec4(elements[0 + colIndex * 4], elements[1 + colIndex * 4], elements[2 + colIndex * 4], elements[3 + colIndex * 4]);
}*/
mat4 mat4::identity() {
return mat4(1.0f);
}

mat4 operator*(mat4 left, const mat4 &right) {
return left.mul(right);
}

mat4 &mat4::operator*=(const mat4 &other) {
return mul(other);
}

mat4 mat4::orthographic(float left, float right, float bottom, float top, float near, float far) {
mat4 result(1);
result.elements[0 + 0 * 4] =  2.0f / (right - left);
result.elements[1 + 1 * 4] =  2.0f / (top - bottom);
result.elements[2 + 2 * 4] = -2.0f / (far - near);
result.elements[0 + 3 * 4] = (left + right) / (left - right);
result.elements[1 + 3 * 4] = (bottom + top) / (bottom - top);
result.elements[2 + 3 * 4] = (far + near)   / (far - near);
//result.elements[3 + 3 * 4] = 1; this is achieved by mat result(1);
return result;
}

mat4 mat4::perspective(float fov, float aspectRatio, float near, float far) {
mat4 result;

float q = 1.0f / tanf(toRadians(fov) / 2.0f);
result.elements[0 + 0 * 4] = q / aspectRatio;
result.elements[1 + 1 * 4] = q;
result.elements[2 + 2 * 4] = (near + far) / (near - far);   // -(far + near)  / (far - near);
result.elements[3 + 2 * 4] = -1;
result.elements[2 + 3 * 4] = 2 * far * near / (near - far); // -2 * far * near / (far - near);

return result;
}

mat4 mat4::translation(const vec3 &translation) {
mat4 result(1.0f); // identity matrix
result.elements[0 + 3 * 4] = translation.x;     // create a matrix as follows: 1 0 0 x
result.elements[1 + 3 * 4] = translation.y;     //                             0 1 0 y
result.elements[2 + 3 * 4] = translation.z;     //                             0 0 1 z
return result;                                  //                             0 0 0 1
}

mat4 mat4::scale(const vec3 &scale) {
mat4 result(1.0f);
result.elements[0 + 0 * 4] = scale.x;     // create a matrix as follows: x 0 0 0
result.elements[1 + 1 * 4] = scale.y;     //                             0 y 0 0
result.elements[2 + 2 * 4] = scale.z;     //                             0 0 z 0
return result;                            //                             0 0 0 1
}

mat4 mat4::rotation(float angle, const vec3 &axis) {
mat4 result(1.0f);
float r = toRadians(angle);
float s = sinf(r);
float c = cosf(r);
result.elements[0 + 0 * 4] = axis.x * (1 - c) + c;
result.elements[1 + 0 * 4] = axis.x * axis.y * (1 - c) + axis.z * s;
result.elements[2 + 0 * 4] = axis.x * axis.z * (1 - c) - axis.y * s;

result.elements[0 + 1 * 4] = axis.y * axis.x * (1 - c) - axis.z * s;
result.elements[1 + 1 * 4] = axis.y * (1 - c) + c;
result.elements[2 + 1 * 4] = axis.y * axis.z * (1 - c) + axis.x * s;

result.elements[0 + 2 * 4] = axis.z * axis.x * (1 - c) + axis.y * s;
result.elements[1 + 2 * 4] = axis.z * axis.y * (1 - c) - axis.x * s;
result.elements[2 + 2 * 4] = axis.z * (1 - c) + c;

return result;
}

std::ostream &operator<<(std::ostream &stream, const mat4 &m) {
stream << "mat4: ( ";
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
stream << m.elements[i + j * 4] << " ";
}
if(i < 3) stream << std::endl << "        ";
else stream << ")";
}
return stream;
}

Мой vec4.h:

#include <iostream>

struct vec4 {
float w, x, y, z;

vec4() = default; // declare a default constructor as a no-parameter constructor (given that I have another one)

vec4(float w, float x, float y, float z);

vec4(const vec4 &v);

vec4 add(const vec4 &other);
vec4 add(float w, float x, float y, float z);
vec4 sub(const vec4 &other);
vec4 sub(float w, float x, float y, float z);
vec4 mul(const vec4 &other);
vec4 mul(float w, float x, float y, float z);
vec4 div(const vec4 &other);
vec4 div(float w, float x, float y, float z);

friend vec4 operator+(vec4 left, const vec4 &right);

friend vec4 operator-(vec4 left, const vec4 &right);

friend vec4 operator*(vec4 left, const vec4 &right);

friend vec4 operator/(vec4 left, const vec4 &right);

vec4 operator+=(const vec4 &other);

vec4 operator-=(const vec4 &other);

vec4 operator*=(const vec4 &other);

vec4 operator/=(const vec4 &other);

bool operator==(const vec4 &other);

bool operator!=(const vec4 &other);

friend std::ostream &operator<<(std::ostream &stream, const vec4 &vector);
};

Мой vec4.cpp:

/*     vec4::vec4() {
w = 0;
x = 0;
y = 0;
z = 0;
}
*/
vec4::vec4(float w, float x, float y, float z) {
this->w = w;
this->x = x;
this->y = y;
this->z = z;
}

vec4::vec4(const vec4 &v) {
this->w = v.w;
this->x = v.x;
this->y = v.y;
this->z = v.z;
}

vec4 vec4::add(const vec4 &other) {
this->w += other.w;
this->x += other.x;
this->y += other.y;
this->z += other.z;
return *this;
}

vec4 vec4::add(float w, float x, float y, float z) {
this->w += w;
this->x += x;
this->y += y;
this->z += z;
return *this;
}

vec4 vec4::sub(const vec4 &other) {
this->w -= other.w;
this->x -= other.x;
this->y -= other.y;
this->z -= other.z;
return *this;
}

vec4 vec4::sub(float w, float x, float y, float z) {
this->w -= w;
this->x -= x;
this->y -= y;
this->z -= z;
return *this;
}

vec4 vec4::mul(const vec4 &other) {
this->w *= other.w;
this->x *= other.x;
this->y *= other.y;
this->z *= other.z;
return *this;
}

vec4 vec4::mul(float w, float x, float y, float z) {
this->w *= w;
this->x *= x;
this->y *= y;
this->z *= z;
return *this;
}

vec4 vec4::div(const vec4 &other) {
this->w /= other.w;
this->x /= other.x;
this->y /= other.y;
this->z /= other.z;
return *this;
}

vec4 vec4::div(float w, float x, float y, float z) {
this->w /= w;
this->x /= x;
this->y /= y;
this->z /= z;
return *this;
}

std::ostream &operator<<(std::ostream &stream, const vec4 &vector) {
stream << "vec4: (" << vector.w << ", " << vector.x << ", " << vector.y << ", " << vector.z << ")";
return stream;
}

vec4 operator+(vec4 left, const vec4 &right) {
return left.add(right);
}

vec4 operator-(vec4 left, const vec4 &right) {
return left.sub(right);
}

vec4 operator*(vec4 left, const vec4 &right) {
return left.mul(right);
}

vec4 operator/(vec4 left, const vec4 &right) {
return left.div(right);
}

vec4 vec4::operator+=(const vec4 &other) {
return add(other);
}

vec4 vec4::operator-=(const vec4 &other) {
return sub(other);

}

vec4 vec4::operator*=(const vec4 &other) {
return mul(other);

}

vec4 vec4::operator/=(const vec4 &other) {
return div(other);

}

bool vec4::operator==(const vec4 &other) {
return (this->w == other.w && this->x == other.x && this->y == other.y && this->z == other.z);
}

bool vec4::operator!=(const vec4 &other) {
return !(*this == other);
}

И журнал ошибок:

.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::identity()’:
.../src/math/mat4.cpp:36:29: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return mat4(1.0f);
^
In file included from .../src/math/mat4.cpp:5:0:
.../src/math/mat4.h:11:16: note: ‘engine::math::mat4::mat4(engine::math::mat4&&)’ is implicitly deleted because the default definition would be ill-formed:
struct mat4 {
^
.../src/math/mat4.h:16:31: error: union member ‘engine::math::mat4::<anonymous union>::columns’ with non-trivial ‘engine::math::vec4::vec4(const engine::math::vec4&)’
vec4 columns[4];
^
.../src/math/mat4.cpp: In function ‘engine::math::mat4 engine::math::operator*(engine::math::mat4, const engine::math::mat4&)’:
.../src/math/mat4.cpp:40:34: error: use of deleted function ‘engine::math::mat4::mat4(const engine::math::mat4&)’
return left.mul(right);
^
In file included from .../src/math/mat4.cpp:5:0:
.../src/math/mat4.h:11:16: note: ‘engine::math::mat4::mat4(const engine::math::mat4&)’ is implicitly deleted because the default definition would be ill-formed:
struct mat4 {
^
.../src/math/mat4.h:16:31: error: union member ‘engine::math::mat4::<anonymous union>::columns’ with non-trivial ‘engine::math::vec4::vec4(const engine::math::vec4&)’
vec4 columns[4];
^
.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::orthographic(float, float, float, float, float, float)’:
.../src/math/mat4.cpp:56:20: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return result;
^
.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::perspective(float, float, float, float)’:
.../src/math/mat4.cpp:69:20: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return result;
^
.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::translation(const engine::math::vec3&)’:
.../src/math/mat4.cpp:77:20: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return result;                                  //                             0 0 0 1
^
.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::scale(const engine::math::vec3&)’:
.../src/math/mat4.cpp:85:20: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return result;                            //                             0 0 0 1
^
.../src/math/mat4.cpp: In static member function ‘static engine::math::mat4 engine::math::mat4::rotation(float, const engine::math::vec3&)’:
.../src/math/mat4.cpp:105:20: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
return result;
^
CMakeFiles/GameEngine.dir/build.make:169: recipe for target 'CMakeFiles/GameEngine.dir/src/math/mat4.cpp.o' failed
make[3]: *** [CMakeFiles/GameEngine.dir/src/math/mat4.cpp.o] Error 1
make[3]: *** Waiting for unfinished jobs....
.../main.cpp: In function ‘int main(int, char**)’:
.../main.cpp:19:50: error: use of deleted function ‘engine::math::mat4::mat4(engine::math::mat4&&)’
mat4 position = mat4::translation(vec3(2,3,4));
^
In file included from .../src/math/math.h:8:0,
from .../main.cpp:4:
.../src/math/mat4.h:11:16: note: ‘engine::math::mat4::mat4(engine::math::mat4&&)’ is implicitly deleted because the default definition would be ill-formed:
struct mat4 {
^
.../src/math/mat4.h:16:31: error: union member ‘engine::math::mat4::<anonymous union>::columns’ with non-trivial ‘engine::math::vec4::vec4(const engine::math::vec4&)’
vec4 columns[4];
^

Я предполагаю, что большая часть кода не имеет значения, поэтому не стоит читать все это.
Просто для сравнения, если я удалю ссылку vec4 columns[4]; от союза в mat4.h, тогда все фантастически.

Я ломал голову над этим в течение последнего часа, поэтому мне действительно нужна помощь.

Благодарю.

РЕДАКТИРОВАТЬ:

После попытки того, что @ 0x499602D2 предложил, а также добавление mat4(mat4&&) = default; до mat4.h у меня осталась только одна ошибка:

.../src/math/mat4.cpp: In function ‘engine::math::mat4 engine::math::operator*(engine::math::mat4, const engine::math::mat4&)’:
.../src/math/mat4.cpp:39:34: error: use of deleted function ‘engine::math::mat4::mat4(const engine::math::mat4&)’
return left.mul(right);
^
In file included from .../src/math/mat4.cpp:5:0:
.../src/math/mat4.h:11:16: note: ‘engine::math::mat4::mat4(const engine::math::mat4&)’ is implicitly declared as deleted because ‘engine::math::mat4’ declares a move constructor or move assignment operator
struct mat4 {
^

Что я могу сделать, чтобы это исправить?