diff --git a/Project.toml b/Project.toml
index de42c02e..97958cff 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "BlockSparseArrays"
 uuid = "2c9a651f-6452-4ace-a6ac-809f4280fbb4"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.7.3"
+version = "0.7.4"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/abstractblocksparsearray/linearalgebra.jl b/src/abstractblocksparsearray/linearalgebra.jl
index 8121477a..70702f0c 100644
--- a/src/abstractblocksparsearray/linearalgebra.jl
+++ b/src/abstractblocksparsearray/linearalgebra.jl
@@ -32,3 +32,102 @@ function LinearAlgebra.tr(a::AnyAbstractBlockSparseMatrix)
   end
   return tr_a
 end
+
+# TODO: Define `SparseArraysBase.isdiag`, define as
+# `isdiag(blocks(a))`.
+function blockisdiag(a::AbstractArray)
+  return all(eachblockstoredindex(a)) do I
+    return allequal(Tuple(I))
+  end
+end
+
+const MATRIX_FUNCTIONS = [
+  :exp,
+  :cis,
+  :log,
+  :sqrt,
+  :cbrt,
+  :cos,
+  :sin,
+  :tan,
+  :csc,
+  :sec,
+  :cot,
+  :cosh,
+  :sinh,
+  :tanh,
+  :csch,
+  :sech,
+  :coth,
+  :acos,
+  :asin,
+  :atan,
+  :acsc,
+  :asec,
+  :acot,
+  :acosh,
+  :asinh,
+  :atanh,
+  :acsch,
+  :asech,
+  :acoth,
+]
+
+# Functions where the dense implementations in `LinearAlgebra` are
+# not type stable.
+const MATRIX_FUNCTIONS_UNSTABLE = [
+  :log,
+  :sqrt,
+  :acos,
+  :asin,
+  :atan,
+  :acsc,
+  :asec,
+  :acot,
+  :acosh,
+  :asinh,
+  :atanh,
+  :acsch,
+  :asech,
+  :acoth,
+]
+
+function initialize_output_blocksparse(f::F, a::AbstractMatrix) where {F}
+  B = Base.promote_op(f, blocktype(a))
+  return similar(a, BlockType(B))
+end
+
+function matrix_function_blocksparse(f::F, a::AbstractMatrix; kwargs...) where {F}
+  blockisdiag(a) || throw(ArgumentError("`$f` only defined for block-diagonal matrices"))
+  fa = initialize_output_blocksparse(f, a)
+  for I in blockdiagindices(a)
+    fa[I] = f(a[I]; kwargs...)
+  end
+  return fa
+end
+
+for f in MATRIX_FUNCTIONS
+  @eval begin
+    function Base.$f(a::AnyAbstractBlockSparseMatrix)
+      return matrix_function_blocksparse($f, a)
+    end
+  end
+end
+
+for f in MATRIX_FUNCTIONS_UNSTABLE
+  @eval begin
+    function initialize_output_blocksparse(::typeof($f), a::AbstractMatrix)
+      B = similartype(blocktype(a), complex(eltype(a)))
+      return similar(a, BlockType(B))
+    end
+  end
+end
+
+function LinearAlgebra.inv(a::AnyAbstractBlockSparseMatrix)
+  return matrix_function_blocksparse(inv, a)
+end
+
+using LinearAlgebra: LinearAlgebra, pinv
+function LinearAlgebra.pinv(a::AnyAbstractBlockSparseMatrix; kwargs...)
+  return matrix_function_blocksparse(pinv, a; kwargs...)
+end
diff --git a/test/test_factorizations.jl b/test/test_factorizations.jl
index 222ae1c1..b934f7e9 100644
--- a/test/test_factorizations.jl
+++ b/test/test_factorizations.jl
@@ -1,6 +1,12 @@
 using BlockArrays: Block, BlockedMatrix, BlockedVector, blocks, mortar
 using BlockSparseArrays:
-  BlockSparseArray, BlockDiagonal, blockstoredlength, eachblockstoredindex
+  BlockSparseArrays,
+  BlockDiagonal,
+  BlockSparseArray,
+  BlockSparseMatrix,
+  blockstoredlength,
+  eachblockstoredindex
+using LinearAlgebra: LinearAlgebra, Diagonal, hermitianpart, pinv
 using MatrixAlgebraKit:
   diagview,
   eig_full,
@@ -22,10 +28,87 @@ using MatrixAlgebraKit:
   svd_trunc,
   truncrank,
   trunctol
-using LinearAlgebra: LinearAlgebra, Diagonal, hermitianpart
 using Random: Random
 using StableRNGs: StableRNG
-using Test: @inferred, @testset, @test
+using Test: @inferred, @test, @test_broken, @test_throws, @testset
+
+@testset "Matrix functions (T=$elt)" for elt in (Float32, Float64, ComplexF64)
+  rng = StableRNG(123)
+  a = BlockSparseMatrix{elt}(undef, [2, 3], [2, 3])
+  a[Block(1, 1)] = randn(rng, elt, 2, 2)
+  a[Block(2, 2)] = randn(rng, elt, 3, 3)
+  MATRIX_FUNCTIONS = BlockSparseArrays.MATRIX_FUNCTIONS
+  MATRIX_FUNCTIONS = [MATRIX_FUNCTIONS; [:inv, :pinv]]
+  # Only works when real, also isn't defined in Julia 1.10.
+  MATRIX_FUNCTIONS = setdiff(MATRIX_FUNCTIONS, [:cbrt])
+  MATRIX_FUNCTIONS_LOW_ACCURACY = [:acoth]
+  for f in setdiff(MATRIX_FUNCTIONS, MATRIX_FUNCTIONS_LOW_ACCURACY)
+    @eval begin
+      fa = $f($a)
+      @test Matrix(fa) ≈ $f(Matrix($a)) rtol = √(eps(real($elt)))
+      @test fa isa BlockSparseMatrix
+      @test issetequal(eachblockstoredindex(fa), [Block(1, 1), Block(2, 2)])
+    end
+  end
+  for f in MATRIX_FUNCTIONS_LOW_ACCURACY
+    @eval begin
+      fa = $f($a)
+      if !Sys.isapple() && ($elt <: Real)
+        # `acoth` appears to be broken on this matrix on Windows and Ubuntu
+        # for real matrices.
+        @test_broken Matrix(fa) ≈ $f(Matrix($a)) rtol = √eps(real($elt))
+      else
+        @test Matrix(fa) ≈ $f(Matrix($a)) rtol = √eps(real($elt))
+      end
+      @test fa isa BlockSparseMatrix
+      @test issetequal(eachblockstoredindex(fa), [Block(1, 1), Block(2, 2)])
+    end
+  end
+
+  # Catch case of off-diagonal blocks.
+  rng = StableRNG(123)
+  a = BlockSparseMatrix{elt}(undef, [2, 3], [2, 3])
+  a[Block(1, 1)] = randn(rng, elt, 2, 2)
+  a[Block(1, 2)] = randn(rng, elt, 2, 3)
+  for f in MATRIX_FUNCTIONS
+    @eval begin
+      @test_throws ArgumentError $f($a)
+    end
+  end
+
+  # Missing diagonal blocks.
+  rng = StableRNG(123)
+  a = BlockSparseMatrix{elt}(undef, [2, 3], [2, 3])
+  a[Block(2, 2)] = randn(rng, elt, 3, 3)
+  MATRIX_FUNCTIONS = BlockSparseArrays.MATRIX_FUNCTIONS
+  # These functions involve inverses so they break when there are zeros on the diagonal.
+  MATRIX_FUNCTIONS_SINGULAR = [
+    :log, :acsc, :asec, :acot, :acsch, :asech, :acoth, :csc, :cot, :csch, :coth
+  ]
+  MATRIX_FUNCTIONS = setdiff(MATRIX_FUNCTIONS, MATRIX_FUNCTIONS_SINGULAR)
+  # Dense version is broken for some reason, investigate.
+  MATRIX_FUNCTIONS = setdiff(MATRIX_FUNCTIONS, [:cbrt])
+  for f in MATRIX_FUNCTIONS
+    @eval begin
+      fa = $f($a)
+      @test Matrix(fa) ≈ $f(Matrix($a)) rtol = √(eps(real($elt)))
+      @test fa isa BlockSparseMatrix
+      @test issetequal(eachblockstoredindex(fa), [Block(1, 1), Block(2, 2)])
+    end
+  end
+
+  SINGULAR_EXCEPTION = if VERSION < v"1.11-"
+    # A different exception is thrown in older versions of Julia.
+    LinearAlgebra.LAPACKException
+  else
+    LinearAlgebra.SingularException
+  end
+  for f in setdiff(MATRIX_FUNCTIONS_SINGULAR, [:log])
+    @eval begin
+      @test_throws $SINGULAR_EXCEPTION $f($a)
+    end
+  end
+end
 
 function test_svd(a, (U, S, Vᴴ); full=false)
   # Check that the SVD is correct