diff --git a/linear_ops/src/macros/matrix.rs b/linear_ops/src/macros/matrix.rs
index c04e965..69db874 100644
--- a/linear_ops/src/macros/matrix.rs
+++ b/linear_ops/src/macros/matrix.rs
@@ -4,18 +4,18 @@ macro_rules! impl_matrix {
 	() => {
 		impl<const X:usize,const Y:usize,T> Matrix<X,Y,T>{
 			#[inline(always)]
-			pub const fn new(array:[[T;X];Y])->Self{
+			pub const fn new(array:[[T;Y];X])->Self{
 				Self{array}
 			}
 			#[inline(always)]
-			pub fn to_array(self)->[[T;X];Y]{
+			pub fn to_array(self)->[[T;Y];X]{
 				self.array
 			}
 			#[inline]
-			pub fn from_rows(rows:[Vector<X,T>;Y])->Self
+			pub fn from_cols(cols:[Vector<Y,T>;X])->Self
 			{
 				Matrix::new(
-					rows.map(|row|row.array),
+					cols.map(|col|col.array),
 				)
 			}
 			#[inline]
@@ -40,38 +40,45 @@ macro_rules! impl_matrix {
 				)
 			}
 			#[inline]
-			// MatY<VecX>.MatX<VecZ> = MatY<VecZ>
+			// old (list of rows)    MatY<VecX>.MatX<VecZ> = MatY<VecZ>
+			// new (list of columns) MatX<VecY>.MatZ<VecX> = MatZ<VecY>
 			pub fn dot<const Z:usize,U,V>(self,rhs:Matrix<Z,X,U>)->Matrix<Z,Y,V>
 			where
 				T:core::ops::Mul<U,Output=V>+Copy,
 				V:core::iter::Sum,
 				U:Copy,
 			{
-				let mut array_of_iterators=rhs.array.map(|axis|axis.into_iter().cycle());
-				Matrix::new(
-					self.array.map(|axis|
+				let mut array_of_iterators=self.array.map(|axis|axis.into_iter().cycle());
+				Matrix{
+					array:rhs.array.map(|rhs_axis|
 						core::array::from_fn(|_|
-							// axis dot product with transposed rhs array
-							axis.iter().zip(
-								array_of_iterators.iter_mut()
-							).map(|(&lhs_value,rhs_iter)|
-								lhs_value*rhs_iter.next().unwrap()
-							).sum()
+							array_of_iterators
+								.iter_mut()
+								.zip(rhs_axis.iter())
+								.map(|(lhs_iter,&rhs_value)|
+									lhs_iter.next().unwrap()*rhs_value
+								).sum()
 						)
 					)
-				)
+				}
 			}
 			#[inline]
-			// MatY<VecX>.VecX = VecY
+			// MatX<VecY>.VecY = VecX
 			pub fn transform_vector<U,V>(self,rhs:Vector<X,U>)->Vector<Y,V>
 			where
 				T:core::ops::Mul<U,Output=V>,
 				V:core::iter::Sum,
 				U:Copy,
 			{
+				let mut array_of_iterators=self.array.map(|axis|axis.into_iter());
 				Vector::new(
-					self.array.map(|axis|
-						Vector::new(axis).dot(rhs)
+					core::array::from_fn(|_|
+						array_of_iterators
+							.iter_mut()
+							.zip(rhs.array.iter())
+							.map(|(lhs_iter,&rhs_value)|
+								lhs_iter.next().unwrap()*rhs_value
+							).sum()
 					)
 				)
 			}
@@ -82,7 +89,7 @@ macro_rules! impl_matrix {
 		{
 			#[inline(always)]
 			pub const fn from_value(value:T)->Self{
-				Self::new([[value;X];Y])
+				Self::new([[value;Y];X])
 			}
 		}
 
@@ -98,13 +105,13 @@ macro_rules! impl_matrix {
 		impl<const X:usize,const Y:usize,T:core::fmt::Display> core::fmt::Display for Matrix<X,Y,T>{
 			#[inline]
 			fn fmt(&self,f:&mut core::fmt::Formatter)->Result<(),core::fmt::Error>{
-				for row in &self.array[0..Y]{
+				for col in &self.array[0..X]{
 					core::write!(f,"\n")?;
-					for elem in &row[0..X-1]{
+					for elem in &col[0..Y-1]{
 						core::write!(f,"{}, ",elem)?;
 					}
 					// assume we will be using matrices of size 1x1 or greater
-					core::write!(f,"{}",row.last().unwrap())?;
+					core::write!(f,"{}",col.last().unwrap())?;
 				}
 				Ok(())
 			}
@@ -166,14 +173,14 @@ macro_rules! impl_matrix_extend {
 	( $x: expr, $y: expr ) => {
 		impl<T> Matrix<$x,$y,T>{
 			#[inline]
-			pub fn extend_row(self,value:Vector<$x,T>)->Matrix<$x,{$y+1},T>{
+			pub fn extend_column(self,value:Vector<$y,T>)->Matrix<{$x+1},$y,T>{
 				let mut iter=self.array.into_iter().chain(core::iter::once(value.array));
 				Matrix::new(
 					core::array::from_fn(|_|iter.next().unwrap()),
 				)
 			}
 			#[inline]
-			pub fn extend_column(self,value:Vector<$y,T>)->Matrix<{$x+1},$y,T>{
+			pub fn extend_row(self,value:Vector<$x,T>)->Matrix<$x,{$y+1},T>{
 				let mut iter_rows=value.array.into_iter();
 				Matrix::new(
 					self.array.map(|axis|{
diff --git a/linear_ops/src/matrix.rs b/linear_ops/src/matrix.rs
index 2c7dfb5..200d176 100644
--- a/linear_ops/src/matrix.rs
+++ b/linear_ops/src/matrix.rs
@@ -2,7 +2,7 @@ use crate::vector::Vector;
 
 #[derive(Clone,Copy,Debug,Hash,Eq,PartialEq)]
 pub struct Matrix<const X:usize,const Y:usize,T>{
-	pub(crate) array:[[T;X];Y],
+	pub(crate) array:[[T;Y];X],
 }
 
 crate::impl_matrix!();
diff --git a/linear_ops/src/tests/fixed_wide.rs b/linear_ops/src/tests/fixed_wide.rs
index ae11c41..7032fd0 100644
--- a/linear_ops/src/tests/fixed_wide.rs
+++ b/linear_ops/src/tests/fixed_wide.rs
@@ -1,4 +1,4 @@
-use crate::types::{Matrix3,Matrix2x3,Matrix4x3,Matrix2x4,Vector3};
+use crate::types::{Matrix3,Matrix3x2,Matrix3x4,Matrix4x2,Vector3};
 
 type Planar64=fixed_wide::types::I32F32;
 type Planar64Wide1=fixed_wide::types::I64F64;
@@ -37,28 +37,28 @@ fn wide_vec3_length_squared(){
 
 #[test]
 fn wide_matrix_dot(){
-	let lhs=Matrix4x3::new([
+	let lhs=Matrix3x4::new([
 		[Planar64::from(1),Planar64::from(2),Planar64::from(3),Planar64::from(4)],
 		[Planar64::from(5),Planar64::from(6),Planar64::from(7),Planar64::from(8)],
 		[Planar64::from(9),Planar64::from(10),Planar64::from(11),Planar64::from(12)],
-	]);
-	let rhs=Matrix2x4::new([
+	]).transpose();
+	let rhs=Matrix4x2::new([
 		[Planar64::from(1),Planar64::from(2)],
 		[Planar64::from(3),Planar64::from(4)],
 		[Planar64::from(5),Planar64::from(6)],
 		[Planar64::from(7),Planar64::from(8)],
-	]);
+	]).transpose();
 	// Mat3<Vec4>.dot(Mat4<Vec2>) -> Mat3<Vec2>
 	let m_dot=lhs*rhs;
 	//In[1]:= {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}} . {{1, 2}, {3, 4}, {5, 6}, {7, 8}}
 	//Out[1]= {{50, 60}, {114, 140}, {178, 220}}
 	assert_eq!(
 		m_dot.array,
-		Matrix2x3::new([
+		Matrix3x2::new([
 			[Planar64Wide1::from(50),Planar64Wide1::from(60)],
 			[Planar64Wide1::from(114),Planar64Wide1::from(140)],
 			[Planar64Wide1::from(178),Planar64Wide1::from(220)],
-		]).array
+		]).transpose().array
 	);
 }
 
diff --git a/linear_ops/src/tests/tests.rs b/linear_ops/src/tests/tests.rs
index 41233b2..573fe9a 100644
--- a/linear_ops/src/tests/tests.rs
+++ b/linear_ops/src/tests/tests.rs
@@ -1,4 +1,4 @@
-use crate::types::{Vector2,Vector3,Matrix4x3,Matrix2x4,Matrix2x3,Matrix3x2};
+use crate::types::{Vector2,Vector3,Matrix3x4,Matrix4x2,Matrix3x2,Matrix2x3};
 
 #[test]
 fn test_bool(){
@@ -21,10 +21,10 @@ fn test_arithmetic(){
 
 #[test]
 fn matrix_transform_vector(){
-	let m=Matrix3x2::new([
+	let m=Matrix2x3::new([
 		[1,2,3],
 		[4,5,6],
-	]);
+	]).transpose();
 	let v=Vector3::new([1,2,3]);
 	let transformed=m*v;
 	assert_eq!(transformed.array,Vector2::new([14,32]).array);
@@ -32,28 +32,28 @@ fn matrix_transform_vector(){
 
 #[test]
 fn matrix_dot(){
-
-	let rhs=Matrix2x4::new([
+	// All this code was written row major and I converted the lib to colum major
+	let rhs=Matrix4x2::new([
 								[  1.0,  2.0],
 								[  3.0,  4.0],
 								[  5.0,  6.0],
 								[  7.0,  8.0],
-	]);						 // |	  |		|
-	let lhs=Matrix4x3::new([ // |	  |		|
+	]).transpose();						 // |	  |		|
+	let lhs=Matrix3x4::new([ // |	  |		|
 		[1.0, 2.0, 3.0, 4.0],//	[ 50.0, 60.0],
 		[5.0, 6.0, 7.0, 8.0],//	[114.0,140.0],
 		[9.0,10.0,11.0,12.0],//	[178.0,220.0],
-	]);
+	]).transpose();
 	// Mat3<Vec4>.dot(Mat4<Vec2>) -> Mat3<Vec2>
 	let m_dot=lhs*rhs;
 	//In[1]:= {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}} . {{1, 2}, {3, 4}, {5, 6}, {7, 8}}
 	//Out[1]= {{50, 60}, {114, 140}, {178, 220}}
 	assert_eq!(
 		m_dot.array,
-		Matrix2x3::new([
+		Matrix3x2::new([
 			[50.0,60.0],
 			[114.0,140.0],
 			[178.0,220.0],
-		]).array
+		]).transpose().array
 	);
 }