diff --git a/python/taichi/_kernels.py b/python/taichi/_kernels.py
index 8043cc5e0de9a..dc7d88b43dc9c 100644
--- a/python/taichi/_kernels.py
+++ b/python/taichi/_kernels.py
@@ -71,10 +71,11 @@ def vector_to_fast_image(img: template(), out: ndarray_type.ndarray()):
         r, g, b = 0, 0, 0
         color = img[i, img.shape[1] - 1 - j]
         if static(img.dtype in [f16, f32, f64]):
-            r, g, b = min(255, max(0, int(color * 255)))
+            r, g, b = min(255, max(0, int(color * 255)))[:3]
         else:
             static_assert(img.dtype == u8)
-            r, g, b = color
+            r, g, b = color[:3]
+
         idx = j * img.shape[0] + i
         # We use i32 for |out| since OpenGL and Metal doesn't support u8 types
         if static(get_os_name() != 'osx'):
diff --git a/python/taichi/math/mathimpl.py b/python/taichi/math/mathimpl.py
index 085e7d169ff2b..9561ffd74bd7b 100644
--- a/python/taichi/math/mathimpl.py
+++ b/python/taichi/math/mathimpl.py
@@ -10,44 +10,44 @@
 
 import taichi as ti
 
-vec2 = ti.types.vector(2, float)  # pylint: disable=E1101
-"""2D float vector type.
-"""
+_get_uint_ip = lambda: ti.u32 if impl.get_runtime(
+).default_ip == ti.i32 else ti.u64
 
-vec3 = ti.types.vector(3, float)  # pylint: disable=E1101
-"""3D float vector type.
-"""
 
-vec4 = ti.types.vector(4, float)  # pylint: disable=E1101
-"""4D float vector type.
-"""
+def vec2(*args):
+    """2D floating vector type.
+    """
+    return ti.types.vector(2, float)(*args)  # pylint: disable=E1101
 
-ivec2 = ti.types.vector(2, int)  # pylint: disable=E1101
-"""2D int vector type.
-"""
 
-ivec3 = ti.types.vector(3, int)  # pylint: disable=E1101
-"""3D int vector type.
-"""
+def vec3(*args):
+    """3D floating vector type.
+    """
+    return ti.types.vector(3, float)(*args)  # pylint: disable=E1101
 
-ivec4 = ti.types.vector(4, int)  # pylint: disable=E1101
-"""4D int vector type.
-"""
 
-mat2 = ti.types.matrix(2, 2, float)  # pylint: disable=E1101
-"""2x2 float matrix type.
-"""
+def vec4(*args):
+    """4D floating vector type.
+    """
+    return ti.types.vector(4, float)(*args)  # pylint: disable=E1101
 
-mat3 = ti.types.matrix(3, 3, float)  # pylint: disable=E1101
-"""3x3 float matrix type.
-"""
 
-mat4 = ti.types.matrix(4, 4, float)  # pylint: disable=E1101
-"""4x4 float matrix type.
-"""
+def ivec2(*args):
+    """2D signed int vector type.
+    """
+    return ti.types.vector(2, int)(*args)  # pylint: disable=E1101
 
-_get_uint_ip = lambda: ti.u32 if impl.get_runtime(
-).default_ip == ti.i32 else ti.u64
+
+def ivec3(*args):
+    """3D signed int vector type.
+    """
+    return ti.types.vector(3, int)(*args)  # pylint: disable=E1101
+
+
+def ivec4(*args):
+    """4D signed int vector type.
+    """
+    return ti.types.vector(4, int)(*args)  # pylint: disable=E1101
 
 
 def uvec2(*args):
@@ -68,6 +68,24 @@ def uvec4(*args):
     return ti.types.vector(4, _get_uint_ip())(*args)  # pylint: disable=E1101
 
 
+def mat2(*args):
+    """2x2 floating matrix type.
+    """
+    return ti.types.matrix(2, 2, float)(*args)  # pylint: disable=E1101
+
+
+def mat3(*args):
+    """3x3 floating matrix type.
+    """
+    return ti.types.matrix(3, 3, float)(*args)  # pylint: disable=E1101
+
+
+def mat4(*args):
+    """4x4 floating matrix type.
+    """
+    return ti.types.matrix(4, 4, float)(*args)  # pylint: disable=E1101
+
+
 @ti.func
 def mix(x, y, a):
     """Performs a linear interpolation between `x` and `y` using
@@ -611,12 +629,46 @@ def length(x):
     return x.norm()
 
 
+@ti.func
+def determinant(m):
+    """Alias for :func:`taichi.Matrix.determinant`.
+    """
+    return m.determinant()
+
+
+@ti.func
+def inverse(mat):  # pylint: disable=R1710
+    """Calculate the inverse of a matrix.
+
+    This function is equivalent to the `inverse` function in GLSL.
+
+    Args:
+        mat (:class:`taichi.Matrix`): The matrix of which to take the inverse.
+
+    Returns:
+        Inverse of the input matrix.
+
+    Example::
+
+        >>> @ti.kernel
+        >>> def test():
+        >>>     m = mat3([(1, 1, 0), (0, 1, 1), (0, 0, 1)])
+        >>>     print(inverse(m))
+        >>>
+        >>> test()
+        [[1.000000, -1.000000, 1.000000],
+         [0.000000, 1.000000, -1.000000],
+         [0.000000, 0.000000, 1.000000]]
+    """
+    return mat.inverse()
+
+
 __all__ = [
     "acos", "asin", "atan2", "ceil", "clamp", "cos", "cross", "degrees",
-    "distance", "dot", "e", "exp", "eye", "floor", "fract", "ivec2", "ivec3",
-    "ivec4", "length", "log", "log2", "mat2", "mat3", "mat4", "max", "min",
-    "mix", "mod", "normalize", "pi", "pow", "radians", "reflect", "refract",
-    "rot2", "rot3", "rotate2d", "rotate3d", "round", "sign", "sin",
-    "smoothstep", "sqrt", "step", "tan", "tanh", "uvec2", "uvec3", "uvec4",
-    "vec2", "vec3", "vec4"
+    "determinant", "distance", "dot", "e", "exp", "eye", "floor", "fract",
+    "inverse", "ivec2", "ivec3", "ivec4", "length", "log", "log2", "mat2",
+    "mat3", "mat4", "max", "min", "mix", "mod", "normalize", "pi", "pow",
+    "radians", "reflect", "refract", "rot2", "rot3", "rotate2d", "rotate3d",
+    "round", "sign", "sin", "smoothstep", "sqrt", "step", "tan", "tanh",
+    "uvec2", "uvec3", "uvec4", "vec2", "vec3", "vec4"
 ]
diff --git a/tests/python/test_api.py b/tests/python/test_api.py
index af554afcbd266..a83b600d9fc89 100644
--- a/tests/python/test_api.py
+++ b/tests/python/test_api.py
@@ -98,13 +98,13 @@ def _get_expected_matrix_apis():
 ]
 user_api[ti.math] = [
     'acos', 'asin', 'atan2', 'cconj', 'cdiv', 'ceil', 'cexp', 'cinv', 'clamp',
-    'clog', 'cmul', 'cos', 'cpow', 'cross', 'csqrt', 'degrees', 'distance',
-    'dot', 'e', 'exp', 'eye', 'floor', 'fract', 'ivec2', 'ivec3', 'ivec4',
-    'length', 'log', 'log2', 'mat2', 'mat3', 'mat4', 'max', 'min', 'mix',
-    'mod', 'normalize', 'pi', 'pow', 'radians', 'reflect', 'refract', 'rot2',
-    'rot3', 'rotate2d', 'rotate3d', 'round', 'sign', 'sin', 'smoothstep',
-    'sqrt', 'step', 'tan', 'tanh', 'uvec2', 'uvec3', 'uvec4', 'vec2', 'vec3',
-    'vec4'
+    'clog', 'cmul', 'cos', 'cpow', 'cross', 'csqrt', 'degrees', 'determinant',
+    'distance', 'dot', 'e', 'exp', 'eye', 'floor', 'fract', 'inverse', 'ivec2',
+    'ivec3', 'ivec4', 'length', 'log', 'log2', 'mat2', 'mat3', 'mat4', 'max',
+    'min', 'mix', 'mod', 'normalize', 'pi', 'pow', 'radians', 'reflect',
+    'refract', 'rot2', 'rot3', 'rotate2d', 'rotate3d', 'round', 'sign', 'sin',
+    'smoothstep', 'sqrt', 'step', 'tan', 'tanh', 'uvec2', 'uvec3', 'uvec4',
+    'vec2', 'vec3', 'vec4'
 ]
 user_api[ti.Matrix] = _get_expected_matrix_apis()
 user_api[ti.MatrixField] = [