diff --git a/sycl/doc/extensions/experimental/sycl_ext_matrix/sycl_ext_oneapi_matrix.asciidoc b/sycl/doc/extensions/experimental/sycl_ext_matrix/sycl_ext_oneapi_matrix.asciidoc
index 57d9066616f8b..f7d916a05144f 100644
--- a/sycl/doc/extensions/experimental/sycl_ext_matrix/sycl_ext_oneapi_matrix.asciidoc
+++ b/sycl/doc/extensions/experimental/sycl_ext_matrix/sycl_ext_oneapi_matrix.asciidoc
@@ -252,11 +252,12 @@ layout.
 ```c++
 namespace sycl::ext::oneapi::experimental::matrix {
 
-template <typename Group, typename T, size_t Rows, size_t Cols,
+// T1 must be the same as T2
+template <typename Group, typename T1, typename T2, size_t Rows, size_t Cols,
           access::address_space Space, access::decorated IsDecorated>
 void joint_matrix_store(Group g,
-   const joint_matrix<Group, T, use::accumulator, Rows, Cols, layout::dynamic> &res,
-   multi_ptr<T, Space, IsDecorated> dest, size_t stride, layout Layout);
+   const joint_matrix<Group, T1, use::accumulator, Rows, Cols, layout::dynamic> &res,
+   multi_ptr<T2, Space, IsDecorated> dest, size_t stride, layout Layout);
 
 } // namespace sycl::ext::oneapi::experimental::matrix
 ```
@@ -371,15 +372,17 @@ joint_matrix_apply(sg, C, [=](T &x) {
 });
 ```
 
-=== Support for the TF32 Data Type
-Some devices support the TF32 floating point type for matrix
-elements. This type has a 19 bit format with one sign bit, 8 exponent
-bits (offering the same range as float), and 10 mantissa bits
-(offering the same precision as sycl::half). Use of this type can
-accelerate the joint_matrix_mad operation by reducing its
-precision. In order to declare a `joint_matrix` object with this
-element type, use `matrix::precision::tf32` in place of the `T`
-template parameter.
+=== Support for Machine Learning Types
+Some devices support special matrix element types that are commonly
+used in machine learning algorithms.
+These types are unusual because the type of the matrix element is
+different from the way the data is stored in memory. As a result, each
+of these elements has two types. There is an abstract identifier for
+the element type, which is an incomplete type defined in the
+`sycl::ext::oneapi::experimental::matrix::precision` namespace, and
+there is a corresponding storage format type. The following synopsis
+lists the abstract types and the table shows the associated storage
+format type.
 
 ```c++
 namespace sycl::ext::oneapi::experimental::matrix::precision {
@@ -389,94 +392,85 @@ class tf32;
 } // namespace sycl::ext::oneapi::experimental::matrix::precision
 ```
 
-For example:
+[frame="none",options="header",cols="20%,20%,60%"]
+|======================
+| `joint_matrix` element type | Storage type | Descritpion
+|precision::tf32 | float | The TF32 type has a 19 bit format with one
+sign bit, 8 exponent bits (offering the same range as float), and 10
+mantissa bits (offering the same precision as sycl::half).
+|======================
+
+In order to declare a `joint_matrix` with one of these element types,
+use the abstract type like so:
 
 ```c++
 joint_matrix<sub_group, precision::tf32, use::a, tM, tK,
              layout::row_major> tA;
 ```
 
-Whenever the application loads, stores, fills, or accesses the
-elements of a TF32 matrix, the application sees the elements as
-float. There are special overloads of these functions for TF32 for
-this purpose.
+Operations on these matrices use the functions described above, but
+there are different constraints on the template parameters as
+described below.
 
-==== TF32 load
-These overloads of `joint_matrix_load` load float values into a TF32
-matrix. It is unspecified whether the implementation loads all 32 bits
-into the joint matrix or if it only loads the relevant 19 bits.
+==== load
+The template parameter `T2` must either be the storage format type
+that corresponds to the abstract type `T1` or it must be a
+const-qualified version of that storage format type. For example:
 
 ```c++
-namespace sycl::ext::oneapi::experimental::matrix {
+joint_matrix<sub_group, precision::tf32, use::a, tM, tK, layout::row_major> tA;
 
-template <typename Group, size_t Rows, size_t Cols,
-          access::address_space Space, access::decorated IsDecorated>
-void joint_matrix_load(Group g,
-    joint_matrix<Group, precision::tf32, use::accumulator, Rows, Cols,
-    layout::dynamic> &res,
-    multi_ptr<const float, Space, IsDecorated> src, size_t stride, layout Layout);
+float *buf = malloc_shared<float>(M*K, q);
+auto pBuf = address_space_cast<sycl::access::address_space::global_space,
+                               sycl::access::decorated::no>(buf);
 
-template <typename Group, size_t Rows, size_t Cols,
-          access::address_space Space, access::decorated IsDecorated>
-void joint_matrix_load(Group g,
-    joint_matrix<Group, precision::tf32, use::accumulator, Rows, Cols,
-    layout::dynamic> &res,
-    multi_ptr<float, Space, IsDecorated> src, size_t stride, layout Layout);
+joint_matrix_load(sg, tA, pBuf + Offset, Stride);
+```
 
-// Only available when Layout != layout::dynamic
-template <typename Group, size_t Rows, size_t Cols,
-          use Use, layout Layout,
-          access::address_space Space, access::decorated IsDecorated>
-void joint_matrix_load(Group g,
-    joint_matrix<Group, precision::tf32, Use, Rows, Cols, Layout> &res,
-    multi_ptr<const float, Space, IsDecorated> src, size_t stride);
+==== store
+The template parameter `T2` must be the storage format type that
+corresponds to the abstract type `T1`. For example:
 
-// Only available when Layout != layout::dynamic
-template <typename Group, size_t Rows, size_t Cols,
-          use Use, layout Layout,
-          access::address_space Space, access::decorated IsDecorated>
-void joint_matrix_load(Group g,
-    joint_matrix<Group, precision::tf32, Use, Rows, Cols, Layout> &res,
-    multi_ptr<float, Space, IsDecorated> src, size_t stride);
+```c++
+joint_matrix<sub_group, precision::tf32, use::accumulator, tM, tK> tC;
 
-} // namespace sycl::ext::oneapi::experimental::matrix
+float *buf = malloc_shared<float>(M*K, q);
+auto pBuf = address_space_cast<sycl::access::address_space::global_space,
+                               sycl::access::decorated::no>(buf);
+
+joint_matrix_store(sg, tA, pBuf + Offset, Stride, layout::row_major);
 ```
 
-==== TF32 store
-This overload of joint_matrix_store stores float values from a TF32
-matrix.
+==== fill
+The template parameter `Tv` must be implicitly convertible to the
+storage format type that corresponds to the abstract type `T`. For example:
 
 ```c++
-namespace sycl::ext::oneapi::experimental::matrix {
-
-template <typename Group, size_t Rows, size_t Cols,
-          access::address_space Space, access::decorated IsDecorated>
-void joint_matrix_store(Group g,
-   const joint_matrix<Group, precision::tf32, use::accumulator, Rows,
-                      Cols,  layout::dynamic> &res,
-   multi_ptr<float, Space, IsDecorated> dest, size_t stride, layout Layout);
-
-} // namespace sycl::ext::oneapi::experimental::matrix
+joint_matrix<sub_group, precision::tf32, use::a, tM, tK, layout::row_major> tA;
+float v = 42.0;
+joint_matrix_fill(sg, tA, v);
 ```
 
-==== TF32 fill
-When `joint_matrix_fill` is called for a TF32 matrix, the type `Tv`
-(the type of the fill value) must be implicitly convertible to
-`float`. It is unspecified whether the implementation writes all 32
-bits of the value into the joint matrix or if it only writes the
-relevant 19 bits.
+==== copy
+There is no special constraint for the `joint_matrix_copy`
+function. The template parameters `T1` and `T2` correspond to the
+element types of the `src` and `dest` matrices.
 
-==== TF32 element-wise operations
-When `joint_matrix_apply` is called for a TF32 matrix, the Callable
-object func is called with a single argument of type `float &`. When the
-application changes this value, it is unspecified whether the
-implementation writes back all 32 bits of the element into the joint
-matrix or if it only write the relevant 19 bits.
+```c++
+joint_matrix<sub_group, precision::tf32, use::a, tM, tK, layout::row_major> tA;
+joint_matrix<sub_group, float, use::accumulator, tM, tK> tC;
+joint_matrix_copy(sg, tC, tA);
+```
 
-In the example below, `C` is a joint matrix of type `precision::tf32`.
+==== Element-wise operations
+The Callable function type `F` must be invocable with a single argument
+whose type is a reference to the storage format type that corresponds
+to the abstract type `T`. For example, in the case where `C` is a
+joint matrix of type `precision::tf32`:
 
 ```c++
-joint_matrix_apply(sg, C, [=](float &x) {
+joint_matrix<sub_group, precision::tf32, use::accumulator, tM, tK> tC;
+joint_matrix_apply(sg, tC, [=](float &x) {
     x *= alpha;
 });
 ```
@@ -887,7 +881,8 @@ is shown in a single column in the table below.
 This is currently available in devices with the architecture
 `architecture::intel_gpu_pvc`, `architecture::intel_gpu_dg2_g10`,
 `architecture::intel_gpu_dg2_g11`, and
-`architecture::intel_gpu_dg2_g12`. In these architectures'
+`architecture::intel_gpu_dg2_g12`.
+In these architectures'
 implementation, the type of the C matrix must be the same as the type
 of the D matrix. Therefore, that common type is shown in a single
 column in the table below.
@@ -897,27 +892,32 @@ column in the table below.
 | A type | B type | C and D type | M | N | K | device
 .2+| `matrix_type::uint8`  .2+| `matrix_type::uint8` .2+|
 `matrix_type::sint32`  .2+|  +<=+ 8 |  16 .2+|  32
-|`architecture::intel_gpu_pvc`|8|`architecture::intel_gpu_dg2_g10,
+|`architecture::intel_gpu_pvc`
+|8|`architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`
 .2+| `matrix_type::uint8`  .2+| `matrix_type::sint8` .2+|
 `matrix_type::sint32`  .2+|  +<=+ 8 |  16 .2+|  32 |
-`architecture::intel_gpu_pvc`|8|`architecture::intel_gpu_dg2_g10,
+`architecture::intel_gpu_pvc`
+|8|`architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`
 .2+| `matrix_type::sint8`  .2+| `matrix_type::uint8` .2+|
 `matrix_type::sint32`  .2+|  +<=+ 8 |  16 .2+|  32 |
-`architecture::intel_gpu_pvc`|8|`architecture::intel_gpu_dg2_g10,
+`architecture::intel_gpu_pvc`
+|8|`architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`
 .2+| `matrix_type::sint8`  .2+| `matrix_type::sint8` .2+|
 `matrix_type::sint32`  .2+|  +<=+ 8 |  16 .2+|  32 |
-`architecture::intel_gpu_pvc`|8|`architecture::intel_gpu_dg2_g10,
+`architecture::intel_gpu_pvc`
+|8|`architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`
 .2+|`matrix_type::fp16`       .2+|  `matrix_type::fp16`   .2+|
 `matrix_type::fp32`   .2+|  +<=+ 8 |  16   .2+|  16 |
-`architecture::intel_gpu_pvc`|8| `architecture::intel_gpu_dg2_g10,
+`architecture::intel_gpu_pvc`
+|8| `architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`
 .4+|  `matrix_type::bf16`       .4+|  `matrix_type::bf16`   .4+|
-`matrix_type::fp32`  | 16 | 16 | 16 .3+|`architecture::intel_gpu_pvc` |
-32 | 64 | 16
+`matrix_type::fp32`  | 16 | 16 | 16 .3+|`architecture::intel_gpu_pvc`
+|32 | 64 | 16
 .2+|  +<=+ 8 |  16   .2+|  16
 |8 | `architecture::intel_gpu_dg2_g10,
 architecture::intel_gpu_dg2_g11, architecture::intel_gpu_dg2_g12`